I had the same experience in the middle of the desert in New Mexico about 20 years ago while on vacation with my wife. It was late at night and we saw two lights which hovered overhead, then one started to move left slowly while the other took off to the right and upward at an extremely high rate of speed. The light which had turned left stopped on a dime and chased the other across the night sky. There were no clouds, we had not been drinking, and there was no swamp gas. I don't know if these were alien ships or experimental aircraft of some kind. If the latter, then the Air Force is doing a very good job of keeping secrets about planes that can fly at an incredible speed.
I have read accounts from some pilots who have reported seeing flying objects moving in similar fashion and at a similar velocity. They were moving so fast they created the same visual sensation you get when quickly waving a sparkler in the air on 4th of July and the light forms a line in the darkness to your eyes.