Nelson Riddle, 64, an Oscar-winning composer and arranger who was probably best known for his work with singers Frank Sinatra and Linda Ronstadt and for his "Theme From Route 66," died Oct. 6 at a hospital here. He had liver and kidney ailments.

He won an Oscar in 1975 for music adaptation for the score of "The Great Gatsby," based on the F. Scott Fitzgerald novel. He also composed the scores for the movies "St. Louis Blues," "Come Blow Your Horn" and "Paint Your Wagon."

Mr. Riddle won two Grammys, the first in 1958 for "Cross-Country Suite," and the second for Ronstadt's "What's New" album. His 1962 composition, "Theme from Route 66," reached No. 3 on Billboard's pop charts that year, and was one of the first television show themes to be recorded and commercially released.

Among the most famous works he arranged was Nat (King) Cole's ballad single, "Mona Lisa," and Sinatra's 1958 album, "Only the Lonely."

Mr. Riddle also had arranged songs for Judy Garland.

But it was his work with Sinatra that brought Mr. Riddle his greatest fame, both on records and on TV, where he provided the music for "The Frank Sinatra Show" from 1950-52 on CBS and from 1957-58 on ABC.

Mr. Riddle and his orchestra also provided the music for a number of television shows, including "The Untouchables," "Route 66," the "Smothers Brothers Comedy Hour," "Rowan & Martin's Laugh-in," "The Leslie Uggams Show," "The Tim Conway Show," "The Julie Andrews Hour" and "The Helen Reddy Show."

In recent years, he and Ronstadt had collaborated on two albums, "What's New?" and "Lush Life," which included richly orchestrated old standards. In 1983, the "What's New?" album became the No. 3-selling LP in the United States, selling more than 3.5 million copies.

The "Lush Life" album in 1984 sold more than 1.5 million copies. Mr. Riddle had recently completed a third album with Ronstadt that is slated for release later this year.

He was born Nelson Smock Riddle on June 1, 1921, in Hackensack, N.J. A piano and trombone player, he joined the Jerry Wald and later the Charlie Spivak orchestras in 1940, moving up to Tommy Dorsey's Band in 1944. His first big hit came in 1956 with "Lisbon Antigua," a crisp piano solo backed by one of Mr. Riddle's deeply chorded arrangements. It made it to No. 1 on the charts for three weeks and was followed a month later by his "Port Au Prince."

Although he became a staff arranger for NBC in Hollywood in the late 1940s and music director of Capitol Records during the 1950s, he first became prominent during the 1950s from his free-lance arranging-conducting on record sessions, especially for Sinatra and Cole.

His first wife, Doreen Moran Riddle, died in 1980. Survivors include his wife, Naomi, and six children by his first marriage.