There are three processes for adopting a child internationally.
Two separate processes apply only to children adopted by U.S. citizens. Depending on what country you choose to adopt from will determine which process you will adopt by.
Hague
Orphan (Non-Hague)
Another process applies to a U.S. citizen or permanent resident who may petition for his/her adoptive child through an Immediate Relative Petition.
Each year our office learns of cases in which lawful permanent residents (LPRs) of the United States have legally adopted a child in another country and then found out that the child cannot join them in the United States. Generally an LPR wishing to adopt a child who is not a U.S. citizen or LPR will have more options to apply for an adopted child to join them in the U.S. if they first become a U.S. citizen through naturalization.
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...an LPR may bring an adopted foreign-born child to the United States based on an approved Form I-130 immigrant visa petition in the immigrant category "F2A" if the adopted child meets the definition of "child" in Section 101(b)(1)(E) of the Immigration and Nationality Act (INA). That section of law requires: 1) the child be adopted while under the age of 16, 2) that the child has been in the legal custody of at least one adoptive parent for at least two years, and 3) that the child has resided with the same adoptive parent(s) for at least two years. These requirements must be satisfied before the LPR adoptive parent(s) may file an immigrant visa petition for the child.
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Legal adoption and ability to obtain an immigrant visa for that child can often be two very separate prospects. There are many factors that affect it - some are listed below.
Is the adopter a US citizen?
Was the child legally adopted?
Does the child have a living parent?
What age was the child when the legal adoption was completed?
Has the adopter lived for two years with the child prior to the petition?