Cornelia Otis Skinner, 78, the Broadway actress, playwright, biographer and humorist, died yesterday in her New York City apartment after a stroke.

Miss Skinner rose to fame in the 1930s as the star of monodramas which she wrote, produced, and in which she inevitably played a variety of persons. Generally historical dramas, they included "The Wives of Henry VIII," "The Loves of Charles II, "The Empress Eugenie," and "Mansions on the Hudson."

A tall, striking beauty, she was known for the lightheartedness of her performances, a talent for the unsettling, and for her barbed wit, with which she poked fun at manners and customs of the time.

She appeared as Mrs. Erlynne in "Lady Windermere's Fan" as Lady Baritomart in "Major Barbara" in London.

Miss Skinner also played Emily Hazen, the wife of an Amercian diplomat, in Lillian Hellman's World War II antiappeasement play, "The Searching Wind." The play opened on Broadway in 1944 and had a run of 326 performances.

In 1958, she starred in a comedy of manners. "The Pleasure of His Company," which she wrote with Samuel Taylor.

Miss Skinner was born in Chicago, Her father was Otis Skinner, one of the finest actors of his day. Her mother, Maude Durbin, was a leading lady in Otis Skinner's company.

She accompnied her parents on the road both in this country and in Europe. She attended Bryn Mawr College where she characterized herself as an indifferent student and cut the final two weeks of her freshman year to join George Tyler's National Theatre Company in Washington.

Miss Skinner later wrote a series of stories for magazines, including the New Yorker, the Atlantic, and Harper's. These articles were later collected in a series of books.

In one of these, "The Ape in Me," published in 1959, she wrote of her Bryn Mawr years:

"I was known as the Tall Girl of my set and the few callow youths who dated me would hardly have been able to let linger a kiss on any feature much above my chin, even if I thrust it forward in the manner of an amorous heifer."

Miss Skinner made her Broadway debut as a member of her Father's company in "Blood and Sand" at the Empire Theater, in 1921. Following the first performance, her father came up to her and said, "Now you're on your own."

Four years later, "Captain Fury," a play she wrote for her father, was produced.During this time her own career was lagging because producers were loathe to give her roles that would be beneath that of the daughter of Otis Skinner. So, she began to write and star in her monodramas.

In her writing, Miss Skinner specialized in chronicling the misadventures that she swore constantly befell her. Perhaps her best known work, written with Emily Kimbrough, was "Our Hearts Were Young and Gay," published in 1942. This was the story of the adventures she had during a trip abroad.

Her other books included "Tiny Gardens," published in 1932, "Dithers and Jitters" in 1938, and "That's Me All Over" in 1941.

She was the author of two biographies, "Madame Sarah," the story of actress Sarah Bernhardt published in 1967, and her last book, about playwrights Howard Lindsay and Russell Crouse, "Life with Lindsay and Crouse" which appeared in 1976.

Miss Skinner wrote scripts for the radio prgoram "William and Mary," and appeared as an expert on the radio program "Information Please."

As a person who was quick at spotting the ridiculous and the false in familiar situations, she was in demand as a speaker.

She told a meeting of the American Gynecological Society in 1963 that she had a few complaints about gynecologists. She said that she was a nicely brought-up girl" and hearing a stranger say "Will you please go into the next room and take off everything except your shoes and stockings?" cause her some missgiving.

"It wouldn't seem so bad if it weren't for that shoes and stockings clause! To my impressionable mind it has always smacked of the more erotic refinements of Berlin during its decadence," she said.

Miss Skinner had been on the executive committee of the Actors Fund and was a director of the Animal Medical Center in New York. She was awarded a plaque for leadership as national chairman of the 1960 observance of National Brotherhood Week by the National Conference of Christians and Jews.

She was a member of the Cosmopolitan and Colony clubs in New York.

Her husband, Alden S. Blodget, died several years ago. Survivors include a son, Otis Skinner Blodget. CAPTION: Picture, CORNELIA OTIS SKINNER, 1962 Photo