I have been split from my ex for almost 5 yrs. We were never married and have 2 children together. I live in Texas and I have a child support order on him. He has not paid anything in a year and a half. He does not have a correct address on file with the AG's office and they cannot serve him correctly. And he contunies to miss court dates. He does not see my children and I want his rights taken away. What can I do. He has another life and I guess has no money and time for my kids. I want to raise my kids by myself I need advice please.

Sounds like he doesn't have any rights if he is missing.
While he does have rights legally, he is not pursuing his rights
So what do you hope to accomplish by having his rights taken?

I want to go out of the country and I can't get a hold of him to sign the passport papers for my girls. I do want to move out of state and I can't because he may choose to then pick up the phone and want them. He truly is not doing any justice to my kids.

If he decides he wants them can you prove he is an unfit father?
Does he have a court ordered visitation plan?
I am sure that if it comes down to it you can very likely prove he is unfit just starting on the fact he is not paying support or having visitations.

It is usually pretty hard to terminate parental rights but it sounds like you at least need a day in court with him to resolve this somehow.

Ok, you are not going to get his rights taken away, just not vistiing or not paying is normally not grounds for it.

You can go back and admend the current custody agreement to give you the right to move and the right to travel. If he does not show up for your hearings, here is little reasons he should win.
Sounds like you need an attorney

As said above you can't just have his rights taken away. I really like Fr. Chuck's answer about having the custody agreement changed so that you can move out of state. If he dosen't show up for the court date for that then you should (note I said should) win and be able to move to another state. You also might want to hire a private investigator to try to get his address so that the support can be enforced more efficiently. Have you gone back to court to have it enforced? If he continues to miss court dates eventually, a warrant will be issued for him so that he will be brought in and have to sit in jail until his court date.