I have (2) 525i Cars and both have the same problem.
I have replaced the O2 sensors in both cars and have replaced the O2 heater relays and IMPROVED the problem.
PROBLEM:::: It feels like the timing is being retarded and advanced or the fuel is being richened and leaned when I accelarate or cruise. The fuel economy gauge slightly goes back and forth when this is happening. One of my 5's is a stick and the other is a automatic. I have also replaced the fuel filter on both. Changing the O2 sensor helped the problem on both but it is still there. The automatic kinda feels like someone is holding it back and then letting it go. And the automatic just started showing a check engine light today(PURGE VALVE)"what does this do?" I ordered a new purge valve today and should be in in 3 days. I am devoted BMW owner, PLEASE someone help me with these problems, I also am a devoted member of the BMWCCA. Thanks for the help. email me. I will get anything I need to to fix this.