Electrical fault (with radiator fan) in 1987 5-cyl Audi?

I have a 1987 Audi 100 with the 5-cylinder 2 litre engine.
When the coolant has reached operating temperature, the fan goes on normally for several seconds at a time.
The problem is this: when the engine is switched off, the fan goes on again, whether it was just on or not. And it keeps going. Switching the ignition on (without starting the engine) turns the fan off. I haven't left it running long enough to see how long it takes to stop running on its own in case I run down the battery, but I do know that if I disconnect the fan while it's running and reconnect it several hours later the fan willl have stopped.
Also, when the fan is running in this state, it has been difficult to start the car (not enough power to turn the engine) but I think I've sorted that by tightening the -ve connection on the battery.
Does this sound like an electrical fault or possibly a fault with the thermo switch which activates the fan?
Thanks in advance for any suggestions.
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I had an 85 Audi 5000 that had a similar problem, and it turned out to be a stuck fan relay.
You can remove the fan relay temporarily to avoid running down the battery when the engine is off.
Replacing the relay with a new one solved the problem.
I hope it will solve yours...
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OTOH, the OP didn't say if the engine is actually the 2.2L turbo. If that is the case, it has a turbo after run pump and it also activates the radiator fan after the ignition is turned off if the coolant temperature is high enough. If this is the case it could run for a number of minutes before turning off.
Still, it might just be a stuck relay like you suggest.
Stephen Clark wrote:

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wrote:

No, it's not the turbo version.

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On Fri, 22 Dec 2006 02:27:27 -0600, "Stephen Clark"

I'll certainly give that a try, thanks. The Haynes manual is less than helpful on the subject.
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On Fri, 22 Dec 2006 02:27:27 -0600, "Stephen Clark"

There are actually two fan relays - the smaller type 214 and the larger type 235. Replacing the larger one solved the problem - the fan only runs on for two minutes or so now.
Thanks again!
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Art Ebbe wrote:

Fan speed one and two relays are in the main relay box just in front of the drivers side windshield.
Fan speed three (fastest when the engine is very hot) is a double wide relay in the Aux relay panel under the dash on the drivers side.
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