I a single father of two and the mother has custody of my children. We were never married and she left the kids with me before new years and has not contacted me or the kids. Its going on a little over a month and I was wondering what can I do about getting custody of my kids. Is this also abondonment on her part. If not what constitutes as abondonment?

Yep, it is go down to your courthouse and file for emergency temporary custody.

Bushg is correct, you go to the court house and file for a temporary custody order, ( that gives you the legal right to have them and stops her from just coming back and taking them.

Then of course you will have to go on and file and go back for full custody latter.