Roger Sessions, a towering figure in the world of 20th century music who earned a reputation as a composer's composer and lived long enough to see his strikingly original work finally win substantial public acceptance, died Saturday in the Princeton, N.J., Medical Center. He was 88.

The Brooklyn-born descendant of a Colonial New England family, Mr. Sessions was born in the 19th century and was musically active in every decade of the 20th, both as a composer and as a theorist and teacher credited with exerting powerful influence on other composers.

A youthful prodigy who was himself influenced early in life by Stravinsky and by his own teacher Ernest Bloch, Mr. Sessions was known as a kind of musical maverick who followed his own path, refused to cater to changing public tastes, and won a reputation as point man for the avant garde.

As a consequence of these qualities and characteristics, it was not until the 1960s that Mr. Sessions won from the public the honor, homage and appreciation that had long been accorded him by at least two generations of American composers who were his students.

Representative of the esteem in which he was held by pupils and peers was Aaron Copland's praise of one of the principal works of Mr. Sessions' initial period, the First Piano Sonata (1928-30).

"To know the work well," Copland wrote, "is to have the firm conviction that Sessions has presented us with a cornerstone upon which to base an American music."

As critics and scholars perceived in Mr. Sessions' early work the influence of such giants as Stravinsky, in time they also began to view him as an heir and adapter of the 12-tone technique of another of the 20th century titans, Arnold Schoenberg.

Always, however, such influences as Mr. Sessions received appeared to be transmuted through his own powerful intellect and sensibility, emerging as work that demonstrated quality, complexity and, almost always, a forbidding difficulty.

Through the years both audiences and critics complained that his compositions placed enormous demands on both listeners and performers.

On at least one notable occasion, in Philadelphia in the 1930s, concertgoers, apparently put off by his cerebral modernism and long, unresolved melodic lines, responded to his work with boos.

Although his Violin Concerto (1931-35), which extended the tonal system, was praised by one critic for its "melodic breadth, rhythmic vitality and immediate musical charm," as well as for "craft and invention," it was rarely performed, probably because of its extraordinary difficulty.

In an interview in the late 1960s, Mr. Sessions acknowledged that his work "has always been difficult," but he added that "it's nothing like as difficult to hear or play now as it used to be."

Musical communication, he said on another occasion, "is a two-way proposition in which the listener must be receptive."

To some critics, one of Mr. Sessions' first major works remained his most engaging, the Symphony No. 1, introduced in 1927. Also viewed as particularly accessible was The Black Maskers, the orchestral score he wrote in 1923 for a performance of the Andreyev play. It evolved into a symphonic suite.

In the 1960s, when public acceptance grew rapidly, he saw the premiere of Montezuma, a monumental three-act opera that was 28 years in preparation and often regarded as a career landmark.

Born Dec. 28, 1896, Mr. Sessions had written an opera by the age of 13, graduated from Harvard at the age of 18, and taught there, at Princeton, at Berkeley and at Juilliard, among other places.

Mr. Sessions was awarded the Pulitzer Prize in music in 1982 for Concerto for Orchestra, written the year before. The author of four books, he also received a special Pulitzer citation in 1974 for his life's work. Survivors include a son, a daughter and two grandchildren.