It looks to me like it's a vent hose for the control pressure regulator. Try tracking it down, to see where it connects (on the other side). It should be hose-clamped onto a nipple on the top of a small box mounted on the back of the left hand valve cover. On my car, it just makes a U-turn, and aims back down onto the valve cover. The whole hose is only 5 inches long. I would like to hear how it looks on other people's cars though. I had a Volvo manual that seemed to suggest it should connect to the airbox at some point, but that is not the case on a Delorean. It's not really important at all. I don't think the vent hose is even part of the smog equipment on the car. Does anyone have any other info?