Yes. I pay taxes to both countries. But there is a double tax treaty and provisions in the US tax code (foreign earned income exclusion) that means that I don't actually pay more taxes and essentially (so far) all my taxes have gone to NZ and the US tax bill has been $0 for a long time now.  But I still have to fill out the damn paperwork!

Sorry for the delay replying, there was an inbox bug in gossip.