I've had a couple of people request annulments... Texas is very strict on when an annulment can take place and the requirements typically hit on the fact one of the persons of the marriage could not give consent due to incapacity or incomplete knowledge of the situation. Once that defect is cured, consent is possible and if the person continues to reside with the person and act as married, the marriage will hold.
Reasons Texas will allow an annulment if at the time of the marriage:
(1) The person was under the influence of alcohol or narcotics;
(2) A person is impotent at the time of the marriage and the other did not know;
(3) One person used fraud, duress or force to induce the other to marry them;
(4) One person was mentally incapacitated at the time of marriage;
(5) One person concealed a divorce from the other; and
(6) if the marriage took place during the mandatory 72 hour waiting period between the issuance of the license and the ceremony.
In each of the above cases, the person without capacity or knowledge of the condition must stop living with the other as soon as the condition becomes known, otherwise annulment is not an option.
Another interesting fact about annulments... the parties do not have to follow the mandatory sixty day waiting period that a divorce places on them, the annulment can be over in a matter of days if agreed, and in 45 days after issuance if a trial is properly requested after the answer date.