In 2001, BMW changed its specifications for engine oil to be used in all 1998-and-older engines. This new oil recommendation for your engine was printed in a Technical Service Bulletin released in October of 2001. BMW goes on to state that the use of oil additives is not recommended nor are they necessary for your engine, and even though the maintenance intervals changed to a greater mileage for all 1999-and-newer engines you should still maintain the same service interval for your car.
Recommended Motor Oil for a 1990 BMW 525i
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Use BMW High Performance Synthetic Engine Oil SAE 5W-30, part No. 07 51 0 017 866, or BMW High Performance Mineral Base Oil SAE 15W-40, part No. 07 51 0 017 868