In 1960, Moore joined with Alan Bennett, Jonathan Miller and Peter Cook to perform at the Edinburgh Festival in the revue "Beyond the Fringe", a precursor of sorts to "Monty Python". Their little stage show took on a life of its own, becoming a hit in London and transferring to Broadway where it was honored with a Special Tony Award. Moore and Cook went on to form a long-standing collaboration that encompassed stage, recordings, and screen. Between 1965 and 1970, they appeared together in the occasional BBC series "Not Only ... But Also", creating an array of characters and perfecting their droll (and sometimes ribald) act. The duo also collaborated on several features, beginning with playing brothers in 1966's "The Wrong Box" and co-writing and co-starring in "Bedazzled" (1967), a romp-like take on the Faust legend. After a second stage triumph in "Good Evening/Beyond the Fridge" (1972-73), they joined forced as co-writers and co-stars on the Sherlock Holmes feature "The Hound of the Baskervilles" (1978). When Cook opted to retire early, Moore settled in Los Angeles and achieved stardom in Hollywood in a series of romantic comedies.

American film audiences first really took note of Moore as a lecherous orchestra leader in the Chevy Chase-Goldie Hawn vehicle "Foul Play" (1978). The following year, he skyrocketed to the top as the middle-aged songwriter who pursues a beautiful young woman (Bo Derek) in the hit comedy "10". (Moore replaced the previously cast George Segal who withdrew for personal reasons. Some fifteen years later, the tables were turned when Moore was let go from "The Mirror Has Two Faces" and was replaced by Segal.)

Firmly established as one of the screen's leading comic actors, Moore hit a career highpoint with his amusing turn as the wealthy, spoiled title character in "Arthur" (1981), a performance that netted him a Best Actor Oscar nomination. It was one of those rare instances of actor and role meshing perfectly and audiences embraced the character and his relationships with the poor girl (Liza Minnelli) and his loyal manservant (Sir John Gielgud). In fact, Arthur came to be seen as Moore's signature role and he spent the next several years playing variants of the slightly lecherous, tipsy millionaire in a string of romantic roles of varying quality. He was badly miscast as a politician courting the mother of a terminally ill child in the maudlin "Six Weeks" (1982), although his score for the film was of superior quality. Similarly, he could not improve on Rex Harrison's original in the inferior remake of "Unfaithfully Yours" (1984). Moore offered a funny turn as a philanderer juggling a wife and mistress who are simultaneously pregnant in "Micki and Maude" (1985) but a turn as a wisecracking elf in "Santa Clause: The Movie" (1985) and a reprise of his best role in "Arthur II: On the Rocks" (1988) seemed undertaken more for the money than for the quality.

Throughout his film career, Moore continued with his musical career, appearing as guest performer with several world-class orchestras. As the 90s dawned, he joined with renowned conductor Sir Georg Solti to develop and co-host the acclaimed Showtime series "Orchestra!". As his star in films dimmed slightly, Moore attempted to translate his appeal to the small screen but neither of his CBS sitcoms ("Dudley" in 1993 or "Daddy's Girls" in 1994) caught on with viewers. Around the time of the cancellation of the latter, Moore began to experience health problems, becoming unsteady on his feet and suffering short-term memory loss. Although there were whispered rumors of substance abuse, the truth was far more devastating. Initially, doctors felt Moore had suffered a series of strokes and they also recommended surgery to repair a small hole in heart. While recovering from the operation in 1998, a neuro-opthalmologist diagnosed a rare brain disease called progressive supranuclear palsy (PSP). While PSP itself isn't fatal, it can lead to opportunistic illnesses. Moore went public with his diagnosis in September 1999. Although retaining a sense of humor about his illness, he was also clearly devastated to no long be able to play music, commenting "It's a great emptiness [in my life]." Moore continued, however, to campaign for a cure, issuing a CD of his music, "Dudley Moore - Live From an Airplane Hangar" in 2000 (with some sale proceeds split between two charitable organizations) and being feted by luminaries like Lauren Bacall, Chevy Chase, Cleo Laine and Barbara Walters with "An All-Star Salute to Dudley Moore" for his birthday in 2001.