I had the same question a while back and asked my service guy at Towne BMW (outside Buffalo, NY) to check 'em out. Sure 'nuf, they only turn to the right, and according to the test, were "working as designed. all normal". I checked out the manual, as well, and found the lights behaving as described. Then I read the foregoing and decided to test em again myself. Now, I can confirm the previous comments - they DO, indeed, turn to the left when the car is moving. They're great!

Anyway, with only an MA degree, I have concluded from this and other similar experiences, that this d___ car is a whole lot smarter than me. I just sit back and enjoy it!

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Sageriders
2011 328, Water [blue], Saddle
2006 X5 4.4i, Sterling Grey/Truffle, Premium, Sport, Cold, Rear, Adj. Ride Ht.
2005 X5 3.0, Sterling Grey/Black, Sport(Totalled!)
2002 330i, Grey-Green Met/Truffle Br. [Sold]