Apart from exchanges, we don't tend to employ people from other countries in our armed forces.
Except when it suits our purposes. We employed a fair number of ex RNZAF personnel in 2001, at the time of their employment none of them had citizenship - they got that after 4? years service. There were 2 of them on 19 Sqn when I went through and damn good they were too.
Made life quite interesting when one got posted to Jags and had issues when he needed access to documents that were PM Secret UK eyes only :P