As long as you are an US citizen - you should report all your income world wide.
Earnings are generally taxable - however if the same income is taxed abroad - you may claim a credit for taxes paid in the foreign country. The form 1116 should be used - http://www.irs.gov/pub/irs-pdf/f1116.pdf
Please let me know if any clarification needed.
As an American citizen or Green Card holder you are subject to U.S. taxation of worldwide income, no matter where you go. However, tax can generally be reduced or eliminated by the foreign earned income exclusion, the housing exclusion and the foreign tax credit, if you qualify for these.
The foreign earned income exclusion may be available if: you are a bona fide resident of a foreign country, or you are physically outside the U.S. for 330 days out of any 365 day period and your tax home is abroad.
As of tax year 2007, this entitles you to exclude up to $85,700 of earned income (i.e., income from working). If your earned income is above $85,700, you may also be eligible for a housing exclusion (generally if you rent), and a foreign tax credit.
So while you may be entitled to certain credits which could reduce or even totally eliminate your U.S. tax liability, you are still subject to U.S. tax and need to file a return.
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