RONNIE BURNS

I wondered this too, I don't remember Ronnie ever being mentioned until he showed up.

Ronnie, became a near-regular on their television show, playing himself but cast as a young drama student who tended to look askance at his parents' comedy style. However, he made a guest appearance on the October 18, 1954 episode ("Gracie Gives Wedding in Payment of a Favor") playing a character named "Jim Goodwin" prior to his debut as a regular, and was formally introduced to the audience at the episode's conclusion. Their daughter, Sandy, was somewhat shy and not too fond of show business. Sandy declined efforts to get her on the show as a regular cast member, though she appeared in a few episodes as a classmate of Ronnie. In one episode, Ronnie's drama class puts on a vaudeville show to raise funds for the school. Gracie hosts the show while Ronnie and Sandy deliver an impersonation of their famous parents along with one of their classic routines. Since Ronnie played himself, Gracie closed the segment with a wisecrack: "The boy was produced by Burns and Allen."

Ronnie popped up in the second episode of the sixth season. Although he'd done a couple of cameos prior to that as an extra, he really wasn't acknowledged in the scripts prior to that. (However, after one such appearance, Gracie did note in their comic routine at the end that "The boy was produced by Burns and Allen.")

George and Gracie had temporarily moved to the St. Moritz in NYC while their house in Beverly Hills was being renovated, according to the storyline. Ronnie showed up upon their arrival, announcing he'd come there as well to attend the Actors' Studio in hopes of becoming a successful dramatic actor instead of following in his parents' comic footsteps, which he deemed beneath him.

They moved into the new house in the seventh season.