Whether you are a 2 year or 10 year green card holder , you are treated as a resident / citizen for tax purposes. There are no limitations to how you legaly earn your living. You are taxed on your world income and foreign income is taxed just like domestic ( i.e. US sourced ) income. If you pay taxes to a foreign taxing authority for your income then you are eligible to recognize that tax either as a deduction ( if you itemize ) or foreign tax credit. Hope this helps
