The now-retired teacher, 78, most recently starred in six episodes of the TV drama The Rich and the Ruthless.
Conway had already played Kenickie, Danny’s best friend, in the stage version of Grease before being cast in the film adaptation.
He later went on to appear in the 1985 limited drama The Insiders as well as the sitcom Flying Blind.
His passing marked one of the first major deaths of the main Grease cast.
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