First off let me say this. I spent a short bit of time in Germany and this is what happened when I had the chance to drive on the autobahn one time. It was a week day and it was in the evening. We had spent a long time in one of the towns visiting and had started heading back to another town where we had a hotel which was reachable a lot faster by using the autobahn instead of using side roads and such. Probably saved about 20 minutes of driving this way. It was during the winter time so it got darker a lot earlier then it did during the summer time in Germany.
To start this off I'll say that it was around mid November about 8 or 9 pm if I remember right. Was riding with two friends, one in the passenger seat and one in the back seat, and they were both passed out due to all the walking and exploring that day while we were visiting the town. I had the head lights on and was driving down the autobahn when I saw these headlights coming up behind me and I was expecting a car needing to pass and so I waited and watch, because I was going to merge over and pass the car I was behind at this time.
I saw the lights come up in my mirror and then nothing. No one passed and no car was visible. There were no exits off of the autobahn at this time and when I checked over my shoulder there were no more lights or anything to show that a car was there. And at this time there was just the car in front of me and we didn't have any cars that were close behind us. The headlights were visible in the mirror up until the rear quarter (where the rear tire is) on the drivers side and then its like they faded away because the light dimmed and eventually disappeared and when I checked over my shoulder there was nothing visible and I looked forward and there was nothing passing the car in front so I merged over and nothing.
I continued the drive to the town we were staying in and got back to the hotel before sitting there thinking about how strange it was. Realizing (I had the window down due to smoking, which I don't believe had anything to do with the experience) that I never heard any motor or anything, which you can usually hear when a car is going about 200 kilometers per hour (about 120 miles per hour) and woke up my buddies and they said that I probably just imagined it.
Feel free to say your thoughts and opinions. I thought it was a pretty interesting experience though.