One of the often overlooked eligibility requirements to obtaining a K1 visa is that there must not be any legal impediments to marriage. In other words, the marriage must be one that would be legal in the U.S. For example if the bride or groom would be ineligible for marriage in the U.S. due to being underage, or a multiple wife in a polygamous relationship for instance, they would be ineligible for a visa even if they would be considered to be eligible for marriage in their home country.
In addition to this point, prior marriages must be properly concluded prior to entering into a subsequent marriage. If either party has previously been married, then evidence must be included which shows that all previous marriage(s) have concluded either by way of divorce, annulment, or death. In this case you should include a copy of the certified final divorce decree(s) (judgment) or death certificate(s). I usually require my clients to obtain these documents before filing with USCIS from either the court or the county which maintains the records if they do not already have a copy because USCIS will likely return to you a request for evidence which places you on a timeline to respond and slows down the case. If these documents are not in English, then a certified translation will be required.
A cautionary note: I have had a couple of clients who after they left prior husbands or wives preferred to assume that they were divorced. In almost all of these cases the presumption proved to be false as no divorce decree had ever been filed for or issued. Do not assume that your prior marriage was dissolved merely because you no longer live with your husband or wife! Moreover, do not choose to try and lie about a prior marriage to the government. Failure to disclose prior marriages can render the beneficiary inadmissible or removable later for making a material misrepresentation. This can happen even if the mistake is discovered after the alien fiancé has become a U.S. citizen!
If you have been confronting any issues dealing with this Eligibility Requirement then feel free to leave a comment here. I will answer any questions that I can in the comments on this post.