Spouse and I were traveling E on I-10 on Dec. 19, 2015. At about 16:00 I noticed an object in the distance. I initially thought it was an aircraft. I was not driving so I continued watching and noticed it did not appear to be moving. Most planes appear to move over time as one is driving. After about 20 min. I asked my spouse to look at the object. We were past Deming, NM, still headed E. I started looking at the object through binoculars, but it was hard to get a fix on it because of the auto movement. We pulled to the roadside at about 16:30.I got a fix on the object and we noted the lat. long. to be approximately 32.20948ºN / 108.08518ºW, near Victorio Mountains which has an above ground level of approximately 815 feet. The object was much higher that the mountain top, and guessed to be 5000'+ above the mountain top.The object was visible through the binoculars and it pretty much filled the field of view. It was white. I would compare it with zinc. It was dumbbell shaped, with one end larger than the other, or perhaps you could say it was peanut shaped with one end larger that the other with a gentle inward curvature at the middle. It also had an armature or long piece coming off of the main body. This was curved upward. The object had rotated slightly and appeared to again be stationary.There were no markings. There was no visible line to tether it in place. It did not bounce nor move in the wind. I have seen commercial blimps in the Phoenix skies numerous times, and this was much larger than a blimp, and was more stable than a blimp trying to be stationary.My spouse has a physics background and has worked with NASA. The object baffled him. He saw what I saw and wondered why other planes were not near because the Holloman AFB and Space Port were not very far away. We observed the object for about 20 minutes and it merely hung in the air. My spouse called it station keeping. It did not demonstrate the nature of a balloon, of a helicopter, or of a blimp. It remained at the same location demonstrating little or no movement. If we were to take a picture, it would have only appeared to have been a white dot in the sky. We decided to press on to Las Cruces. We drove on and a mile or two we reached the turn off for Gage, NM. I kept looking at the object, and eventually had to look over my shoulder. Now it was approximately 16:55 and the sun was going down. I checked and the object did not have ANY lights on it. We assumed if it was an aircraft or a weather balloon, it would have a light. As the sky got darker and darker, I could still see the object and by 17:15, I was too far away to see it any more. We still are perplexed as to what it was.