I have assets, If I marry someone with credit issues can I be incurring their debt?

You can't incur the debt, as it has already been incurred.  You might, however, become LIABLE for the debt if you live in a community property state. The easy way around this is to have a prenuptial agreement done.  In any event, you should direct your question to a family law attorney in your area.  I don't see what this question has to do with bankruptcy law. Mark Markus has been practicing exclusively bankruptcy law in California since 1991.  He is a Certified Specialist in Bankruptcy Law by the State Bar of California Board of Legal Specialization,  AV-Rated by martindale.com, and A+ rated by the Better Business Bureau.