If both spouses are undocumented immigrants

If both spouses are undocumented immigrants, it may be difficult to get legal proof of a valid marriage. US marriage licenses are issued by counties. Most counties require that at least one person show legal identification. This is usually a US driver's license, a US state ID, or a passport. You can check the requirements with your county clerk's office. 

If one spouse is an undocumented immigrant and one spouse is a US citizen

After getting married, an undocumented immigrant becomes an "immediate relative" of their US citizen spouse. This relationship may mean that the undocumented spouse is eligible for a Green Card (also known as a lawful permanent resident).

If eligible for a Green Card, the undocumented spouse can apply to become a conditional permanent resident. This conditional Green Card is only valid for 2 years. To remove the conditions, you must file within the 90-day period before the conditional Green Card expires. You must also show proof that the marriage was entered into in good faith and not for the purpose of avoiding immigration laws.

In general, a person is not eligible for a Green Card if they were not inspected and admitted or paroled by an immigration officer before entering the US. There are other reasons why a person may not be eligible for a Green Card. For more information, visit Green card: deportation and inadmissibility. However, some people may be able to apply for a waiver to ask the government to give them a Green Card even if they are inadmissible. For more information, visit Applying for a waiver of inadmissibility.