stumbles on acceleration

Could be an idea to get a mechanic to check the fuel pump and also pipe. The popping sound is basically it is not coverting the fuel to gas properly. I think the best idea is to have the fuel pump and pipe checked. Hope it helps

Couple things - Ohm testing a MAF is not going to tell you if its bad or good - your need to do a sweep test of it If you just have a meter do whats called a MIN/MAX test ..keep your gauge connected and accelerate the vehicle take a look at your min max readings - If the min reading drops to zero or is significantly lower than your base reading the MAF is junk.( Obviously a scope would be ideal for this test ) ALSO do this with the Throttle position sensor ( TPS) this may have multiple sensors in one unit. You need to check them all Hope this helps. Good Luck

A 1991 525i should have a non-vanos M50 motor....I would begin by checking the resistance of the coils. There is no cap and rotor on that car...its direct ignition and when the coils stop functioning properly they cause all kinds of problems including fuel not combusting properly or at all. Next I would do as one of the previous posters said....check the MAF. From there I would check for vacuum leaks. Take a can of brake cleaner a very lightly spray it close to all the vac hoses with the motor on and if you hear the rpms increase. Increase in rpms means vac leak.

check your spark plugs.. happened to my car.. changed the plugs and problem is gone :)

check your diff, because if the power is not going to the acxcels it sometimes backfires, and your cars computer mine had an issue simular to yours it turned out the the computer is missreading the tbs