In Texas, the grounds to have a marriage annulled are extremely narrow.  Specifically, a court can grant an annulment only if one of the following applies:

1. One of the spouses was under the age of 18  and did not have the appropriate consent or a court order;
2. One spouse was under the influence of drugs or alcohol at the time of the marriage, lacked the capacity to consent as a result, and the parties never lived together after the effects wore off;
3. A party was permanently impotent at the time of marriage, the other spouse did not know, and the parties did not voluntarily live together after the other spouse learned of the impotency;
4. The respondent used fraud, duress or force to induce the petitioner into marriage, and the petitioner has not voluntarily lived with the respondent since learning of the fraud or being released from the duress or force;
5. One of the spouses is mentally incompetent, lacked the ability to consent to the marriage, and the parties have not lived together since the discovery of the mental disease or defect;
6. The respondent divorced a third party within 30 days before the date of marrying petitioner, at the time of marriage the petitioner did not know of the divorce, and since discovery the divorce, the parties have not lived together; or
7. If the parties were married less than 72 hours after issuance of the license, the marriage can be annulled only if filed within 30 days after the marriage.

If none of the above grounds apply, the parties cannot annul the marriage.  Although there are a few other situations where a marriage can be voided (incest, bigamy, a party is a minor, or one party is a current or former step-child of the other), most people looking to dissolve a marriage who cannot get it annulled will need a divorce.