[3] In 1976 he was invited by Birtwistle to become Assistant Music Director of the Royal National Theatre in London.
[5] Muldowney's orchestral music includes a number of concerti (for piano, saxophone, oboe, violin, percussion, trumpet and trombone), many of which explore his fascination with polyrhythms.
Muldowney’s radio opera The Voluptuous Tango (1996) won the Prix Italia in 1997, and the Gold Award for Best Radio Drama at 1997 Sony Drama Awards, and received its stage premiere in Hoxton New Music Days, London in 2000.
Muldowney has written much music for TV, radio and film[6] including The Ploughman’s Lunch (1983), Nineteen Eighty-Four with Richard Burton (1984), The Ginger Tree (1989), Sharpe (1993), The Peacock Spring (1996), King Lear (1997), Bloody Sunday (2002) and Copenhagen (2002).
Until 2006 Muldowney taught composition at the Royal Academy of Music in London.