in order to assess chances, an experienced attorney will need to review the dispositions for all arrests and review the deportation documents. Only then an opinion can be provided.
This is not legal advice and a client attorney relationship is not created. For a free consultation call (718)234-5588.
If he was deported after a conviction for an "aggravated felony" -- a term which needs an immigration attorney to review your documents and explain to you after a review of all the records --- then he will be barred from re-entry indefinitely but may apply for a waiver. If he does not have a permanent bar he will still need a waiver but it really depends on several factors, such as what the convictions were for, whether he has other bars, such as for unlawful presence, etc. You need to consult an AILA immigration attorney to decide whether it is possible or worth the time and expense to try to petition for him at this early date.
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No attorney-client relationship is created or implied by this communication in any way. Consult a competent immigration attorney preferably one who is a member of the American Immigration Lawyers Association (AILA).
Your husband may be eligible for a waiver that would permit him to enter the US again. The only way to determine if this is an option for him would be for an immigration attorney to review the dispositions for all of his arrests and the deportation documents. There are also other factors that will have to be evaluated.
Consult with an attorney.