@Ahtaxquestion , @buddhadude , @dgcarey16 , having read through the original post and comments thereto:
(a) for tax purposes , US does not recognize dual citizenship. Thus as a citizen/resident ( Greencard ) US taxes you on your world income, no matter where earned. So all citizen/Residents must file form 1040 reporting world income.
(b) the tax treaties between US and "the other country" generally are for the purpose of 1. ameliorate double taxation and 2. provide treatment for special circumstances / situation.
(c) for US citizen/Residents earning and living in another country, there is "Foreign Earned Income" exclusion available to reduce the effects of double taxation and foreign tax credit/ deduction for taxes on income still double taxed.
(d) same rules to avoid double taxation apply for countries with whom US does not have a tax treaty, but in such cases there are no protection for special situations.
Bottom line is that as dual citizen you must still file US return to be able to take advantage of , or assert tax treaty conditions, such benefits.
Does this answer your query or do you need situation specific answers ( in which you would need to provide your country of residence, countries of citizenship, your employer whether US government, US private entity, foreign government, foreign private entity, presence type -- how long and plans to return or stay permanently, family situation -- accompanied or not, etc. etc. )
