If your 'gas' cap spins regardless of it being locked or not here is the technique I used to permanently fix the two halves together. This method does not require any external holes, screws, bolts or rivets.
What should be happening: when you unlock your gas cap the lock cylinder pushes the small black plastic 'key' into a slot inside the gas cap.
What actually happens: The small spring fails to force the black plastic 'key' into its slot resulting in the 2 halves of the cap not locking together.
The fix:
I popped the top part of the cap off the lower part, it is a press fit and comes off pretty easily. The lock barrel and a spring will then drop out.
Drive a screw through the plastic lock barrel in line with the broken spring. The right length screw does 2 things, it pushes the black plastic locking piece back to where it should be (permanently) and becomes another locking tab that engages on the opposite side. Choose a screw with a head that will slide into the slot.
Put it all back together and I can guarantee that this will work for another 20 years.
Hopefully the attached photos will make all that talk clear for you.
If you have a cap that you can't unscrew from your tank because it is free-wheeling just carefully lever the top off and you should be able to then unscrew the rest of it with a suitable width piece of steel or a file even.
The first 3 photos show the gas cap top, the white plastic lock cylinder, the rusty screw (that I put there 20 years ago), the lock cylinder spring, and the steel & black plastic threaded body part that the lock cylinder slots into.
The last photo shows the lock cylinder back in the threaded part and ready to clip back together (you can just make out a shiny new screw head on the right).
This is a 1984 fuel cap without the BMW logo, the early ones could be different. (Snowbum has more info about the earlier caps.)
Bruce
Topic: How to fix a fuel, gas, petrol cap explained! (Read 2350 times)