I am a Deputy Sheriff and was on duty shortly after 0500 hrs. in the first part of June 2014. I was parked near the intersection of US Hwy 67 and Texas Hwy 137. I observed a very bright white light slowly approaching from the west. It appeared to be a landing light of an aircraft and I thought it was coming to our airport. I first saw the light at a range of approximately four miles. The light seemed to be about 500 feet off the ground. At about two miles the light slowly started to change to a southeasterly direction as though to keep from flying over the town of Big Lake. As the light got to about 90 degrees to me, I realized that the light was not diminishing in intensity or shape. I thought that was quite unordinary and got out of my patrol vehicle. I watched as the light continued on in a southeasterly direction toward the city of Eldorado in Schleicher County. I watched this very, very bright light for at least ten minutes. It never changed in brightness or shape while approaching, when crossing in front of me, or WHEN GOING AWAY. The light just continued on until I could no longer see it. I believe the light never got closer than 1 or possibly 2 miles. I did tell another deputy about the incident shortly thereafter. No other. [initials removed/cms/dr]