Can I apply for citizenship if I am married to an illegal?

Karla writes, "I received my green card through marriage that ended in divorce after 7 years (yeah, I did not file for naturalization because we never had the money to pay the fees due to his alcoholism) and I now I am ready to apply after saving the money.  In the meantime, I married an undocumented alien and want to naturalize so that I can try to fix his papers.  Will my marriage to an illegal immigrant come to bite me or him or result in his being arrested/deported or my application rejected?"

While the application will ask you to provide complete details about your husband, including his being in the United States illegally, but there are laws in place that will prevent the government from rejecting your application or coming after him (assuming he is not wanted for some serious crimes, the Feds are hunting for him, and will be delighted to find out his whereabouts).  So unless you are married to a terrorist or a criminal on the run, and if you are eligible, you will be approved.  After approval, you must work with an excellent immigration attorney to file his paperwork because his being in the country illegally makes his case harder but not impossible.