Legal Question in Family Law in New Mexico

My first reaction is that such a marriage would be void because to get a license the parties must swear that neither is bound by marriage to another person. But before you rush off and do something rash with that piece of information I would strongly suggest you consult with an attorney to get some careful research into the question, because the situation you describe could have very serious consequences - status of children, property, estates, etc., that could cause a court to want to fashion some equitable remedies. Marriage is a contract and a court may want to apply equitable remedies from contract law to the situation, taking into account the circumstances surrounding the failure to disclose the existing marriage, whether there was in fact an existing marriage, were both parties aware of such.