Robert managed to work a third performing job in Washington Square Park and at the Provincetown Playhouse as a member of the political improvisational guerrilla troupe, "Jack LaRumpa's Flying Drum & Kazoo Band."

After completing the successful Manhattan Theater Club engagement, Hegyes was cast by Tony Award–winning actor Len Cariou (making his directing debut) to co-star in the Broadway drama, Don't Call Back, starring Arlene Francis and Dorian Harewood.

While performing on Broadway, Hegyes auditioned for television producer James Komack and was cast to star in what was to become the award-winning ABC comedy, Welcome Back, Kotter.

Hegyes made his Los Angeles stage debut as "Chico Marx" in the Westwood and national touring company engagements of An Evening with Groucho.

Upon returning from the tour, Hegyes was cast by producer Barney Rosenzweig to star as a series regular portraying undercover detective "Manny Esposito" in Cagney & Lacey.

Hegyes became "Artist-in-Residence" at his alma mater, Rowan University, teaching screenplay writing, acting for camera and public speaking, and was a guest lecturer in the Radio/Television/Film & Theater Departments.

[citation needed] Having returned to live in his hometown of Metuchen, New Jersey in 2009, Hegyes made his last public appearance in early January 2012, reprising his "An Evening with Groucho" role as Chico Marx, this time in three performances of "The Marx Brothers: Flywheel, Shyster and Flywheel," a staged radio play re-creating several episodes of the early-1930s broadcasts.