Yes, you may travel outside the U.S., but if you plan to be abroad for an extended period, e.g. longer than 6 months, you should apply for a reentry permit (Form I-131) before you leave the U.S.

A reentry permit establishes that you did not intend to abandon status, and it allows you to apply for admission to the United States after traveling abroad for up to 2 years without having to obtain a returning resident visa. Reentry permits are normally valid for 2 years from the date of issuance.

You cannot renew a reentry permit while abroad. You can return to the US for a short time and apply for a new one, but subsequent reentry permits may only be approved for one year at a time.

For any extended periods outside the U.S., you should plan ahead with your immigration attorney to get legal advice for your specific facts and goals.

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