Can anybody name a great Australian composer? I don't think so.
Well, it depends on what you might be thinking of as "great", but, among 20th and 21st century composers, there's really quite a fair number of internationally-performed and respected names (and/or people who write fine music, which aren't always the same ones of course), among whom one might mention Don Banks, Gerard Brophy, Warren Burt, Nigel Butterley, Tristram Cary, Barry Conyngham, Edward Cowie, Brett Dean, Chris Dench, Ross Edwards, Mary Finsterer, Andrew Ford, Riccardo Formosa, Jennifer Fowler, Percy Grainger, Richard Hames, Keith Humble, Dominik Karski, Elena Kats-Chernin, Liza Lim, David Lumsdaine, Chris Mann, Thomas Meadowcroft, Richard Meale, Damien Ricketson, Jon Rose, Peter Sculthorpe, Ian Shanahan, Matthew Shlomowitz, Roger Smalley, Michael Smetanin, Carl Vine, Malcolm Williamson, Adam Yee and David Young, to name only those whose music I've actually heard.