Not specifically different for non-US citizens, but people who are non-citizens may fall into various traps that do exist (and vary by location) to include:
1. Lack of SSN
2. Non-residency in the state you're applying for the marriage license
3. Form of identity/proof of age accepted: specifically, a passport that is not in English may require a certified English translation
You should inquire at whoever issues marriage licenses wherever you intend to get married as to the specific requirements. Some of the things may be easier to have the fiance do prior to coming to the US.