Anyone applying for U.S. lawful permanent residence (a green card) based on marriage to a U.S. citizen or lawful permanent resident (the "petitioner") must prove that the marriage is both:
A key part of proving both these things is showing that any prior marriages are well and truly over. The U.S. government worries that someone would, for example, fake a divorce in order to stage a green card marriage with someone new.
Therefore, as part of any marriage-based petition to U.S. Citizenship and Immigration Services (USCIS), you will need to supply proof that any prior marriages, whether of the U.S. petitioner or the intending immigrant, are legally ended.
The normal way to prove this is through documents, such as with an official divorce or death decree. These, you would include with the I-130 petition that starts off the marriage-based immigration process. Simply providing this paperwork might not, however, lead to a smooth or easy result. USCIS has the power to investigate further.
In recent years, USCIS has become doubtful as to whether the documentation it receives showing termination of a prior marriages, particularly divorce decrees, are the real thing. With such documents coming from various countries around the world, it has been difficult for USCIS to assess their credibility and be sure it has detected the fraudulent ones.
However, improved communications technology has given USCIS and other immigration authorities new prospects for investigating a document's source and validity. So, even if you believe you've done everything right, you might find that your immigration case gets delayed, if U.S. immigration authorities start investigating whether your or your current spouse's first marriage really ended.
If USCIS sends you a Request for Evidence (RFE) asking for additional documents to prove that either the U.S. petitioner's or the immigrant's previous marriages have ended, that's a sure sign that the agency is giving your documents a hard look.
This issue can affect applicants not only applying for a green card through marriage, but also later applying for naturalization (U.S. citizenship), if they got their green card through marriage, or even if they got the green card in some other way but now appear to be committing bigamy.
The stakes are high here. If you are seeking a green card based on marriage, and your marriage took place despite your not having received a valid divorce, then your current marriage is invalid and the green card will be denied.
If the previous divorce was valid but you're having trouble proving it, consult an experienced immigration attorney.
Similarly, if you are applying for naturalization, realize that doing so gives USCIS a whole new opportunity to check whether your marriage-based green card was valid, and to assess whether you have the good moral character required for naturalization. See Will You Be Denied U.S. Citizenship Based on Polygamy, Bigamy, or Multiple Marriages? for more information.