My 1999 CLK is possessed. Or so it seems.

Many times, when I leave the car and lock it, thus "arming" the alarm system, here is what happens:

1. The lights blink three times and then turn off, as they should.
2. Then, the lower front lights and tail lights start blinking again, eventually setting off the alarm.

I will then unlock the car, open the door, close it, and start the whole process over, and the same result. So...I now cannot lock my car without the alarm going off a few minutes later.

Does anyone have an idea of what kind of problem I might have?