Legal Question in Family Law in Texas

I'm assuming from the way you ask the question that your marriage took place first? If that's the case, and you remain married, no, he cannot legally marry someone else until your marriage is dissolved somehow, whether he does it via a marriage license and ceremony or by the common-law provisions. The second intended marriage would be and remain invalid until such time as the first one was dissolved.

If I misunderstood and the common-law marriage happened first, officially, the answer's the same, but it would be your marriage that would be invalid (the first one will always remain valid until something happens to dissolve it, and you can't legally be married to more than one person at a time). However, in practice, there are an awful lot of people who are at least potentially common-law married who play it fast and loose with the rules. They typically believe that if they didn't have to have a license and ceremony to be considered married, they don't need a divorce to end their marriage, either. That's not true, but there is a Family Code provision that sort of supports that--if neither spouse takes steps within two years of separation to assert legally that they were married, it's presumed that they weren't, though that presumption can be rebutted. In other words, not getting a divorce after a common-law marriage ends is possibly a legal way to return to "unmarried" status, but it's very, very iffy, and I would never advise a client to just not worry about it.