I have a 1987 535e with 181000 miles on it, the right turn signal will not work.The left one works and I dont see that a fuse is burnt out.Any help?

Check the socket the bulb goes in...My break lights were not working on my bmw and the sockets were rusted you might be able to sand the rust off but with mine they where to far gone...(there like 5 bucks each for a new one) if thats not the issues turn on you blinker and make sure your getting power...and you can always change the bulb i had one that didnt look burned out but it was

There may also be an issue with the turn signal switch itself. If the four way flashers work but the turn signal does not, it may be the turn signal switch on the column. PN 61-31-1-377-987. to replace, remove "button" at the center of the steering wheel by prying it out, remove nut retaining the steering wheel, and then remove the plastic shroud and the under dash cover to access the wiring connectors (non air bag car only)

The left turn signal works, its only the right that does not.Can it be possible that it is broken only on one side?

very possible. the turn signal switch can and will do what you are seeing happen.

I have the same problem the relay clicks but the right light doesnt work...the hazards work but the right one doesnt...it works sometimes but most of the time it will not work....replace the bulbs, sockets, and the bulb in the intrument panel..check all wiring...i'm lost when it comes to this one

Definitely try a turn signal switch to see if the issue goes away.