Hello-
I am wondering what might be causing the air compressor to continue running (sometimes several minutes) after the engine is shut off.
Thanks!
Mark

Is it always running when the car is on? Try hitting the off switch in the trunk by the latch. It should turn itself off after a few minutes of use, if the car is on or off. But it could be that your rear air struts are leaking.

Welcome Mark. First, make sure you put your year (1994) and Model (SSE) in your signature (this is done in your "Profile" and will help aid us in future diagnosis). You may also want to add in where you live since a member may be close by that could help

Now, since you have an SSE, I am assuming you have the Electronic Leveling Control (ELC) option or "air struts" on your bonne. If your struts or the tubing from the compressor to the struts is leaking, then the compessor may continue to run even after the ignition has been turned off. There are many posts about ELC here. You may want to "search" and type in "ELC" for some further posts about this problem that will help you diagnose if/where a leak is.

good old leak

do you happen to park the car on a hill? nose up? this will also cause weight to shift to the back, causing the ELC to kick in and level off the car.