Free range hunts for oryx in New Mexico? Many think you have to travel to Africa to hunt oryx (gemsbok), but New Mexico has a thriving population of them! Oryx offer a thrilling hunt. They can be hunted almost year-round. Hunts are either held “on range” or “off range”, and tags are allocated through the New Mexico Game & Fish lottery draw. Contact us to talk about your oryx hunt in New Mexico!