Mary Martin, America's favorite leading lady of musical comedy, as Ens. Nellie Forbush in "South Pacific," Maria von Trapp in "The Sound of Music" or the title role in "Peter Pan," died Saturday afternoon at her home in Rancho Mirage, Calif. She was 76 years old.

She died of cancer, said Richard Grant, who handles publicity for the actress's son, Larry Hagman. Miss Martin, who had been hospitalized recently at the Eisenhower Medical Center in Rancho Mirage, returned home last Tuesday.

More than any of her peers, she was what she played and she incarnated the songs that she sang. Miss Martin was "a cockeyed optimist" and she was also the eternal child imagined by James M. Barrie. Approaching 70, she was still saying, "I can't help thinking I'm 19." On stage, at least figuratively, she never stopped flying. Echoes of Poetry

In reviewing her performance in "South Pacific," Kenneth Tynan said that she reminded him of something Aldous Huxley wrote about the minor Caroline poets: "They spoke in their natural voices and it was poetry." While Ethel Merman was an entire brass section and Carol Channing was a parade, Miss Martin remained natural and exactingly true to life -- and it was poetry.

Her voice was never the strongest instrument. She was not beautiful (though she could be radiant). Through determination, pluck, charm, self-mocking humor and a profound sense of self, everything converged to create an exhilarating theater artist.

For 50 years Miss Martin projected the vitality of someone who loved her work and knew precisely how to make other people share in her happiness. As Elia Kazan, who directed her in her first Broadway starring role in "One Touch of Venus," said in his autobiography, she was "full of the love of being loved." Specialized in Long Runs

Although she made a number of films, she was devoted to the theater. She starred in relatively few Broadway shows, but the work was valuable; one could regard the actress herself as being the heyday of the Broadway musical.

She specialized in long runs and was known for not missing performances. In his autobiography, Richard Rodgers called her "an extraordinary trouper," adding, "In all the years I've known her, I have never seen her give a performance that was anything less than the best that was in her." She did have, he said, one unusual trait: "She cannot utter even the mildest form of profanity." The "strongest expression" he ever heard her use was "He's a son-of-a-bear."

If there had been a darker side to Miss Martin, she certainly kept it hidden from her public, which never failed to think of her as joyful. In her private life, she endured tragedies (including her husband's death) and on stage was prone to suffer accidents, but she never let anything interfere with the sheer delight of her performance. A Thousand Shampoos

Repeatedly she set herself challenges, many of them physical. It was at her suggestion that Nellie Forbush literally washed that man "right out-a my hair," which meant that she shampooed her hair on stage for 1,000 performances. Originally she had planned to sing another song in "South Pacific" while cartwheeling across the stage -- until she cartwheeled right into the orchestra pit. It was also her idea to sing a song standing on her head in "Jennie," one of her less successful musicals. In rehearsal at the age of 63 in the Aleksei Arbuzov play "Do You Turn Somersaults?," she turned somersaults on stage until she fell from a revolving platform and was grounded by her doctors.

In her autobiography, "My Heart Belongs," she declared that of all her characters Peter Pan was indisputably her favorite, for a very simple reason: "Everyone else loves Peter so." She added, "Neverland is the way I would like real life to be: timeless, free, mischievous, filled with gaiety, tenderness and magic."

The key to her first Broadway success, in 1938 in the Cole Porter musical, "Leave It to Me," was her innate ability to combine innocence and insouciance. In that show she sang "My Heart Belongs to Daddy," a vintage Porter song in which almost every word has a double meaning. She played against the lines, which made them even funnier, and she did a striptease as if she was hanging up the laundry. It was often said about that song that Miss Martin did not know what she was singing until Sophie Tucker, who was also in the cast, explained the worldly, witty lyrics to her. The actress was never to lose that inbred sense of ingenuousness. An Early Flight, A Crash Landing

From the first, Mary Virginia Martin was self-propelled. She was born in Weatherford, Tex., on Dec. 1, 1913 (although some reports placed the date one year later), the younger daughter of Preston Martin, a lawyer, and Juanita Presley Martin, a violin teacher. As one of a trio of little girls dressed as bellhops, she sang on a bandstand outside her father's courtroom. When she was 5, she sang "When Apples Grow on the Lilac Trees" at a fireman's ball. Once she tried to fly -- from the roof of a garage, without the mechanical assistance she would have later as Peter Pan -- and broke her collarbone.

Frequently she sang in churches and at clubs, and learned about show business by watching movies and imitating singers and dancers. As a young woman, she appeared with her best friend, Bessie Mae Sue Ella Yaeger, in amateur theatricals and later wondered why she had become a star and Bessie Mae had not. She decided it was because "I react to an audience.

"Give me 4 people and I'm on . Give me 400 and I'm a hundred times more on."

As a tribute to Bessie Mae -- and for good luck -- she worked her friend's name into many of her scripts, on stage and in films.

In her book Miss Martin recalled that Weatherford was famous for its watermelons. Long after she became a star, a sign was erected on the courthouse lawn: "Weatherford, Texas, home of watermelons and Mary Martin." Her observation: "I never got top billing in my hometown."

Nevertheless she had, she was convinced, a very happy childhood. Her parents sent her to Ward Belmont, a finishing school in Nashville. At 16, she married Benjamin Hagman, a Weatherford accountant and later a lawyer. They had one child, Larry Martin Hagman, who -- as the world knows -- became famous as J. R. on television's "Dallas." Dancing Her Way To Hollywood

The actress's first marriage lasted only a few years, and the teen-age bride brought up her son as if he were her younger brother. Miss Martin was soon caught up in her career. At 18, she opened the Mary Hagman School of Dance in Weatherford, then went to Hollywood to study dancing and to search for a way to enter the movies. For several years she went back and forth between the two states and between teaching and performing.

The dancing school flourished (until it was destroyed by fire) while her performing career took several divergent paths. In Texas she sang on radio; in California she sang and danced in nightclubs. One evening she performed in a Sunday night talent show at the Trocadero nightclub in Los Angeles. Singing "The Weekend of a Private Secretary" and an operatic number entitled "Il Bacio" in her own syncopated version, she created a sensation. To her astonishment, people stood on chairs and tables and shouted bravo. Jack Benny, who was in the audience, later told her that it was one of the most exciting moments he could remember. "In 10 minutes," she said, "my life had changed."

Another member of the audience was Lawrence Schwab, a producer who took charge of her career. In answer to the frequent question, what causes a big break, she said: "Work. Work and work and work; be ready when the break comes." As she wrote in her autobiography, "All my life I have felt guilty if I didn't use any talent I have as fully as I could."

Under Mr. Schwab's aegis, she came to New York and auditioned to fill a suddenly vacant supporting role in the forthcoming Broadway musical "Leave It to Me." The unknown actress strode into a suite in the Ritz Towers and announced that she was going to sing four songs, adding, "If I can't sing all four, I'd rather not sing." As she recalled in her book, "A man reclining on a couch said, very mildly, 'Carry on, on all fours.' " She later discovered that the philosophical man on the couch was Cole Porter, the composer of the show. Bella Spewack, co-author of the book with her husband, Sam Spewack, asked Miss Martin if she had ever been on the New York stage. She admitted that she had not, and when Mrs. Spewack asked her why she thought she could do it, she answered boldly, "Try me."

In the audition, she was called upon to read her character's dialogue. She shouted the first line, "I'd like to renew my subscription" (meaning she would like to continue having a love affair). Her straightforward, self-confident delivery brought down the house. Should she get the part, Mr. Spewack told her, she should never change the reading of the line. Throughout her career her art was founded on such intuition. A First Casting Much Against Type

She so captivated Porter and his collaborators that she was signed, despite the fact -- or rather because of the fact -- that she was cast against type: the innocent country girl playing a kept woman, and singing a striptease showstopper, "My Heart Belongs to Daddy." Fifty years later, in 1988, as a great-grandmother, she was still singing "My Heart Belongs to Daddy," at a celebration honoring Cole Porter. In May 1990 she was scheduled to sing the song again at the 75th anniversary celebration of the Shubert Theater in New Haven, but canceled her appearance because of illness.

Her overnight success on Broadway on Nov. 9, 1938 put her on the cover of Life magazine and drew the attention of Hollywood. Under contract to Paramount, she appeared in a series of forgettable roles in forgettable films, including "The Great Victor Herbert," "Rhythm on the River," "Love Thy Neighbor," "New York Town," "Birth of the Blues," "Kiss the Boys Goodbye," "Happy Go Lucky" and "True to Life."

There was one positive result of her Hollywood experience. She met and married Richard Halliday, a story editor at Paramount. He also became her producer and closest professional adviser and the father of their daughter, Heller Halliday. If she had remained in Hollywood, she might have disappeared into the studio system, but wisdom prevailed and she returned to New York, where she became a Broadway star and remained one for the next four decades.

Her first starring role was in "One Touch of Venus," written by Kurt Weill, Ogden Nash and S. J. Perelman. To combat his wife's hesitancy about playing the title goddess, a role originally conceived for Marlene Dietrich, Mr. Halliday took her to the Metropolitan Museum of Art and showed her the many interpretations of Venus in painting and sculpture. As the "Venus of Ozone Heights," who comes to life and steps down from her pedestal, she had her customary winsomeness, singing her signature song, "That's Him," simply sitting in a chair facing the audience. The Bumpy Road To 'South Pacific'

After "One Touch of Venus," she starred in the musical "Lute Song" and in London in Noel Coward's "Pacific 1860" and toured for a year in Irving Berlin's "Annie Get Your Gun." Though Ethel Merman had played the title character, Annie Oakley, in the original production, the role -- along with the song, "Doin' What Comes Naturally" -- seemed made to measure for Miss Martin. As always, she was undeterred by the fact that she was succeeding another star (which she also did later when she took Carol Channing's "Hello, Dolly!" on tour of military bases in Vietnam).

In 1948, Richard Rodgers and Oscar Hammerstein 2d offered her the central role in "South Pacific." She was hesitant for two reasons. Disliking hospitals, she was not anxious to play the role of a nurse, and she felt insecure because her leading man would be an opera star, Ezio Pinza. When it was decided that the two would not be asked to sing a duet, she accepted the offer. Nellie Forbush, singing "Cockeyed Optimist," "Honey Bun," "I'm Gonna Wash That Man Right Out-a My Hair" and, especially, "I'm in Love With a Wonderful Guy," became one of her greatest successes.

"South Pacific" was followed in 1954 by "Peter Pan" (her daughter was also in the cast) which she performed on Broadway and on television, live and then on tape, complete with her celebrated aerial ballet. The Broadway production ran for only 152 performances. It was largely through the taped television version (which was recently released on videocassette) that she became so identified with the role.

"Peter Pan" was an exact meeting of actress and character. As Miss Martin said, "I cannot even remember a day when I didn't want to be Peter." For years she had dreams of flying, all of which stopped just before the first television presentation of the show. Trying to explain the end of those dreams, she said, "Perhaps it was because I had experienced at last the joy of really flying." She could become almost mystical whenever she spoke about the experience, as in her statement: "I discovered I was happier in the air than on the ground. I probably always will be." Another Character, Another Classic

In 1959, Rodgers and Hammerstein went to her again to ask her to play Maria von Trapp in "The Sound of Music." Though her own background could not have been more dissimilar from that of her real-life model, she -- and the audience -- felt the kinship. As she said, "We both have the same drive, utter determination." During her two years in the role, she missed only one performance.

Of her three Broadway triumphs only "Peter Pan" was to be recorded for posterity -- in the television version.In the case of both "South Pacific" and "The Sound of Music," other actresses played her role on screen (Mitzi Gaynor was Nellie and Julie Andrews was Maria von Trapp.) This meant that, except for her television appearances, especially one dynamic evening teamed with Ethel Merman, her most noteworthy performances existed only on the stage and on records.

As one sign of her own fallibility she often pointed to the fact that while accepting "South Pacific," "Peter Pan" and "The Sound of Music," she turned down the chance to be in "Oklahoma!", "Kiss Me Kate" and "My Fair Lady."

Among her other Broadway shows were the two-character musical "I Do I Do" and "Jennie." Occasionally she acted in dramas -- in a revival of "The Skin of Our Teeth," which she and Helen Hayes took on tour, and in "Do You Turn Somersaults?"

She and her husband owned a ranch in Brazil, Nossa Fazenda (Our Farm), next to a home owned by her friend Janet Gaynor. The Hallidays used the ranch as a vacation retreat. After her husband died in 1973, Miss Martin worked less but never fully retired. In 1981 she was a host on "Over Easy," a public television series about aging. In 1982 she was in a taxicab accident in San Francisco that took the life of her close friend Ben Washer and severely injured Miss Martin, Miss Gaynor and Miss Gaynor's husband, Paul Gregory. In 1986, fully recovered, she returned to the theater in a dramatic role, co-starring with Carol Channing in James Kirkwood's "Legends." Each portrayed an aging actress. "Legends" toured but never came to New York.

In 1989, Miss Martin returned to New York for a tribute to the television work of Richard Rodgers and to see "Jerome Robbins's Broadway," which reprised "I'm Flying" from "Peter Pan." Several months later, the 1960 television version of "Peter Pan" was shown again, with great success. Later, an illness precipitated her withdrawal from "Grovers Corners," Tom Jones and Harvey Schmidt's musical version of "Our Town," in which she was scheduled to play the Stage Manager. In 1989 she received a Kennedy Center Award, given annually at the John F. Kennedy Center for the Performing Arts in Washington. Famous First Line One More Time

Some years ago she participated in a birthday tribute to Richard Rodgers at the Imperial Theater, where, decades before, she had made her Broadway debut in "Leave It to Me." For days, she worried about what she would say. When the time came, in characteristic fashion, she improvised. She walked on stage and said as loudly as she could, "I would like to renew my subscription." When she wrote about this moment in her autobiography, she commented, "That's what I would like to say, now and forever, to all audiences everywhere." Mary Martin's lifetime renewal was gratefully accepted.

Miss Martin is survived by her son, her daughter, Heller Halliday DeMeritt, six grandchildren and one great-granddaughter. Funeral services will be private. A memorial service will be held in New York at a later date.

Mary M Halliday