My question involves divorce in the State of: Texas

I was divorced back in May of 2005. In the decree my ex-husband was awarded about $20,000 from me. I was told to pay 300.00 a month with 6% interest. I have only sent him about $1,000 dollars to date. So far it doesn't seem like he is going to take legal action against me to pay the remainder. However, is there a statue of limitations as far as time goes where lets say after so many years he won't be able to sue me?