[2][3] Szeps studied acting at the Ensemble Theatre during weekends, under the direction of Hayes Gordon, while gaining science and electrical engineering degrees at Sydney University.
In 1963, while studying for a Bachelor of Science in mathematics and physics during the day, he appeared every night at the Ensemble Theatre, in a play called The Physicists, which ran for six months.
Szeps is best known for his role as selfish dentist Robert Beare in the classic Australian television comedy series Mother and Son (1984–1994), with Garry McDonald, Ruth Cracknell and Judy Morris.
Szeps won the Penguin Award for best actor for his role in ABC's 10 part series Palace of Dreams.
He has performed in five one-man shows produced by the Ensemble Theatre, the last three self-penned: The Double Bass (1990), Sky (1992) (written for him by John Misto), I'm Not a Dentist (1997), Why Kids (2003) and Wish I'd Said That (2010).