Noel, am I right in assuming these are budget airbrushes? If so then cleaning is even more important. The cheaper models, while serviceable, tend to not be as well finished as more expensive models. This becomes a problem as the roughter finish on internal parts makes it much easier for paint to accumulate and harden. I have a couple of cheaper brushes that came with my compressor and while they work ok they are a bi*ch to keep clean and are really only suitable for applying coats when respraying. They're not good for detail work.
As Eoin said, cellulose thinners is yer only man for cleaning away paint deposits and sometimes an overnight soak is the only way to get it completely clean.