Piotr,
If you have an existing FAA license there is no problem.
If you have a JAA UK license then in order to fly your
N-reg outside the UK on that JAR-PPL you either need
to have a specific waiver from that country to allow you
to fly there with your UK license, a license for that country
or an FAA certificate derived from your existing UK license.
To get an FAA certificate you need to follow this URL,
http://www1.faa.gov/avr/afs/flightinstruction/5-9-8.htm
where all is explained.
Its a bit of a pain as you have to nominate an American
FSDO to visit in the US to complete your paperwork, but once
done, a permanent certificate will follow,
-- Andrew