He is best known as the drummer and a founding member of 1980s pop/new wave group Men at Work,[1][2] which had Australian, US and UK hits with their singles "Who Can It Be Now?"

After that, Speiser joined pop rockers Frost[2] where he played the drums in the single "You and Me" from their album The Usual Suspects.

Speiser (Drums/vocals) and Ben Fitzgerald (Guitars/vocals) co-founded a guitar-driven style rock band Where's Claire?

In 1990, they were joined by Andrew Midson (Bass/vocals) and Brenden Mason (Guitars/vocals) and released their first commercial album, Long Time Coming, in 2002.

He also formed his own low keyed rock band The Working Stiffs and had a single called "Who Can It Be Down Under?"