During the 1964 presidential campaign, for example, Mr. Allen portrayed the ultraconservative Republican candidate Barry Goldwater — although he made no attempt to sound like him, and began the interview with “Hello dere!” — and said he was confident of winning “all 13 states.”

Within a few years after teaming up in the late 1950s, Allen and Rossi had become a familiar presence in the nation’s top nightclubs and on television variety shows.

Allen & Rossi Video by my2centsish

In two of their many appearances on “The Ed Sullivan Show” — Mr. Allen liked to say that they had been on the show more times than Ed Sullivan himself — Allen and Rossi had the unenviable task of following the Beatles. They won over an audience dominated by screaming teenage girls both times.

On the first occasion, in February 1964, Mr. Allen performed a frenetic dance wearing a Beatle wig; on the second, in September 1965, he ran up and down the aisles while Mr. Rossi sang…

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