New Mexico has a hunting draw system. Every year you apply for the various hunts in the units you want and then in june the game and fish will release the results of the draw.
Those lottery draws are for elk, mule deer, antelope, bighorn, oryx, ibex and javelina.
You can buy a trapper tag over the counter if you want to hunt furbearers.
You can also buy turkey, mountain lion and bear tags over the counter.
Lots of great hunting to be had in NM.
NMDGF