If my fiancé J1 visa will expire soon and we want to get married, how much later can we marry after his visa expires?

Generally, if a foreign national overstays a nonimmigrant visa, like a J-1 visa, he becomes unlawfully present in the U.S. and if he comes to the attention of immigration authorities he may be subjected to removal/deportation proceedings; unlawful presence for 180 days or longer could subject him to a 3-year bar to re-entry into the U.S., and unlawful presence for a year or longer could subject him to a very harsh 10-year bar. Nonetheless, if a foreign national who entered the U.S. lawfully and with inspection, such as with a J-1 visa, becomes married to a U.S. citizen, the couple may pursue a marriage-based adjustment of status application process notwithstanding that the foreign national overstayed an initial visa. In that instance, however, the foreign national would not be eligible to apply for Advance Parole (a "travel document" authorizing travel while the adjustment of status application remains pending). Note also that while a notation on a J-1 visa stating that it is not subject to the two-year home residence requirement may be accurate, it is not dispositive. Depending on factors such as the funding organization for the J-1 visa, it may be advisable to seek an Advisory Opinion Letter confirming the two-year rule does not apply. The application process often can be significantly more complex than it may appear from reading the application forms, their instructions, and the applicable parts of the immigration statute. It would be wise for you and your fiance to consult with an immigration attorney who, after learning all of the relevant details, could advise about eligibilities, options and strategies, and who then could offer legal representation in the application process. Some immigration law firms, including mine, offer legal services on a "flat fee" basis so that a client will know the total expense from the very beginning, and a few immigration law firms, including mine, offer an initial consultation free of charge.