When foreign nationals apply for admission to the U.S. based on marriage, they must usually submit primary evidence in the form of a marriage certificate: a document issued or recognized by the government of the place where the marriage was formed. However, in certain countries, marriage records are "unavailable," as indicated on the U.S. Visa: Reciprocity and Civil Documents by Country page of the Department of State website.
They might be unavailable, in some cases, because the government database was destroyed during a war or natural disaster. For example, in Chad, all official documents were presumed destroyed during the country's 1980 civil war. Or, in other cases, marriages were never registered in the first place, perhaps due to a difference in cultural practice (as in the case of Buddhist couples in Burma, a.k.a. Myanmar) or the absence of a functioning government (as in the case of Somalia).
When official records are unavailable, secondary evidence may be submitted instead (see What If Documents For Your Green Card Application Are Unavailable?). Check the Reciprocity page for your country of marriage to see if it includes specific suggestions in this regard. (For example: Buddhist couples from Burma who execute marriage affidavits or sworn statements in front of a notary public may submit such documents as proof of marriage.)
More generally, unofficial records from key institutions such as schools, hospitals, and clergy, could provide a good alternative. But when such institutional records are also unavailable or unreliable, couples can always strengthen their case by submitting marriage affidavits from relatives, friends and others who attended their wedding, as well as personal, business or other government records reflecting their marital status.
Marriage affidavits submitted by, in order of importance, parents, siblings, extended family members, friends, and other persons who attended a couple's wedding, can help prove the existence of the couple's marriage.
Such affidavits should include a detailed description of the events that occurred during and around the wedding ceremony. In cases involving traditional or religious marriages, in particular, immigration officials could carefully examine that description to make sure that it is consistent with independent accounts of the couple's tradition. For example: For a couple from Somalia (which is a country with a largely clan-based society), the extent to which the marriage brought together different families or clans might be emphasized.
In addition, marriage affidavits should include information about the identity of their author or "affiant" (full name, date and place of birth, and address), as well as information about the affiant's relation to the couple. Ideally, such information should be supported with official proof of identity and family relationship. Unfortunately, family members of couples from countries where records are unavailable are, of course, also likely to lack access to the same type of documents. When this is the case, other forms of secondary evidence become more critical.
When couples petition and apply for U.S. green cards, they are required to prove not only that their marriage exists legally but also that it was entered into in good faith (not just for the purpose of getting immigration benefits for a non-citizen). Conversely, couples who lack evidence that their marriage legally exists could arguably provide evidence of a "good faith" relationship instead.
Such indirect evidence would include personal letters and emails, phone records, residential records, travel records, joint family photographs, joint business records, and other proof that the couple shared the same household or resources. It would also include evidence that the couple has had children.
In fact, any document that mentions or reflects the existence of a marital relationship could serve as secondary evidence. This includes, for instance, previous visa or status applications (even from other countries) that include statements about an applicant's marital status. For example: A Somali refugee who applied for resettlement with her spouse in Europe before being admitted to the U.S. could perhaps submit a copy of that application as evidence of her marriage.
Even marriage certificates issued by governments that are not recognized by the U.S. could sometimes have persuasive weight when combined with other evidence. Marriage documents issued by regional religious courts in Somaliland, for example (a breakaway Somali province) might well informally support affidavits submitted by family members, though such documents are not officially recognized. (Caution: Consult an immigration attorney to determine whether submitting such documents would be good or bad in your particular case.)
In the end, no single piece of secondary evidence is likely to substitute for unavailable official documents. However, couples who submit secondary evidence in large numbers and in various forms stand a better chance of proving their marriage in the absence of such official records.