have a 1987 bmw 325i starts then shutd down right away im stumped please help

Could be a lot of issues, need more information on what you have tested to give a good answer.

Cant be certain with the information given, but I would start by checking the exhaust for restrictions, especially the cat (make sure its not melted down), also maybe try adjusting the top injector screw on the intake plenum, and even do some maintenance to the ignition system if you hear it running rough before it dies.

I have a 325E with a similar problem.  The issue is inter mitant though.  I am able to start the car every time.  Fires right up and runs for a couple seconds then just shuts down.  I have to turn the key all the way off and back on to get the engine to refire but it will start right up immediately everytime but most times it will just shutdown again.  This will happen repeatedly until one time it will stay running and I can drive it for a random amount of time and without warning sometime it feels like it no longer is on.  You can try to rev the engine but will get no response.  There is no chugging like it is not getting the correct fuel or air mixture.  i have checked the fuel pump and it is pumping fuel.  Have not checked the exhaust but it appears to be exhausting gas.  let me know if anyone knows of a good way to check this.  Nothing appears to be burned or clogged.  i get good flow out of the tailpipe.  i get the impression there is a faulty electrical component but not sure.

The dealer tells me they can not recreate what I am seeing and they are telling me I need to replace a coolant sensor.  Could the sensor be bad and causing the engine to think it is overheated and needs to be shutdown?

Thanks

need more detail on the car. eg, history of car,how well maintained is it ?, as it could be alot of issues causing it,

Car is immaculately maintained.  The only thing that looked a bit fishy was oil leaking onto what appeared to be an actuator or controller between the intake manifold and the air filter box.  

Can you recommend a good repair manual for these cars.  We found a haynes manual which are usually really good but it covered so many different makes and years that none of the things in the manual looked like what I was seeing under the hood.

Thanks for the quick reply!

When the car shuts off, does it retain lights, radio, etc?

Try a Chiltons manual. Similar to a Haynes.

Has the car ever been in an accident? My mom had a car, not a BMW, that did the same thing after a minor fender bender. Apparently there is a switch that causes the car to shut off right after starting. I don't know what it is called but it did the same thing.

you could try a robert bentley manual, have a look at one see wat you think.

i would take the car for a diognostic check, for the quickest way to solve the problem.but do fix the oil leak as it cant be doing much good.  

but be careful as some garages will try to pull your pants down with the price. but the problem does sound electrical.

have you phoned a dealer ? the ones over here in england are allways happy to help, and offer advice about any problem. and ive allways found them very helpfull. just tell them the problem and they will tell you what is causing it. and what part you need to get.

and they are not pushy trying to make you bring the car to them, like some dealers. eg, audi.