We visited White Sands National Park and remained late to observe the sunset and the thousands of visible stars. My wife fell asleep and I was driving on the lonely access road near the park. There was nobody around. While driving I noticed two beige lights hovering in the sky to the south so I pulled over, turned off car and lights, got out and closed my door. It was pitch dark. The two lights in the sky moved very slowly in an easterly direction making no noise for about a minute. I could not tell exactly how far away they were but it was probably at least half a mile. Suddenly, one took of to the southwest and upward at a 45% angle at a very high rate of speed. The other light, which was still gliding slowly in an easterly path, made a quick loop motion and give chase to the first light. They climbed out of sight within a few seconds. There were no people around, the sky was totally clear with no clouds, and there are no city lights within 50 miles of that location.This happened 10 years ago. After stumbling across this website I decided to report it. At first, I thought they might have been experimental military aircraft. But the ability of those objects (at least I had the impression that they were objects) to effortlessly make dramatic directional changes and travel at an astonishing rate of speed while making no sound makes me question that assumption.I should add that I am 64 years old, work as a conservative insurance manager, do not drink or take drugs, was not on any prescriptions at the time, and have never had any other unidentified aircraft sort of sightings.