I want to travel to my country due to sm family matters while my case is in process can I travel back to my country?
Yes. Talk to an experienced immigration attorney prior to your departure to discuss any possible issues.
The answer provided is general in nature and should not be construed as legal advice as not all facts are know by the attorney, nor does the answering of this question create an attorney client relationship.
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Yes, you can travel outside the US while the I-751 is pending. Did you receive form I-797 Notice of Action? It extends your conditional resident status for one year (authorizes work and travel) while the application is pending.
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You can travel with your current green card, however you will want to be careful of its expiration date and make sure you can stay informed about your case status and any requests for evidence. If you have previously taken long trips out side the U.s. since getting your green card, or if you plan to take a long trip now (more than a few weeks), you should speak with an attorney about how this will affect your residency and continuous presence.
This answer is intended as public information about a legal topic. Answers posted here do not create an attorney-client relationship. For specific legal advice, please make an appointment to speak with an attorney in private.