The Flynn & Son Funeral Home in Fords, N.J., said it was informed of Hegyes' death Thursday by the actor's family.
A spokesman at JFK Medical Center in Edison, N.J., told the Star-Ledger newspaper that Hegyes, of Metuchen, arrived at the hospital Thursday morning in full cardiac arrest and died.
Hegyes was appearing on Broadway in 1975 when he auditioned for "Kotter," a TV series about a teacher who returns to the inner-city New York school of his youth to teach a group of irreverent remedial students nicknamed the "Sweathogs." They included the character Vinnie Barbarino, played by John Travolta.
The show's theme song, performed by John Sebastian, became a pop hit.
Hegyes also appeared on many other TV series, including "Cagney & Lacey."
He was born in Perth Amboy and grew up in Metuchen, the eldest child of a Hungarian father and Italian mother.
He attended Rowan University, formerly Glassboro State College, in southern New Jersey, before heading to New York City after graduation. He returned to Rowan on several occasions to teach master classes in acting, a university spokesman said Thursday.
"He was a good friend to the university," spokesman Joe Cardona said.
Hegyes continued to act after "Kotter" and was a regular on "Cagney & Lacey." He also guest-starred in shows including "Diagnosis Murder" and "The Drew Carey Show."
On his website, Hegyes wrote that he was inspired by Chico Marx, whom he had played in a touring production of a show about the Marx Bros. He also recalled how his mother encouraged him to get involved in theater as a teen.