DC9 ACFT ON VECTORS FOR APCH WAS TWICE ASSIGNED RWY 21L BY CTLR. WHEN FLC SAW ANOTHER ACFT APPEARED TO BE LINED UP FOR RWY 21L THEY QUESTIONED THE NEW CTLR WHO THEN SAID THE RWY WAS RWY 21R.

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APCH AT DTW TOLD US TO EXPECT A VISUAL TO RWY 21L AT DTW. WE CAME FROM THE MIZAR ARR. WE WERE BEING VECTORED AND OUR POS WAS NW OF THE ARPT. WE AGAIN ASKED APCH TO VERIFY OUR RWY. THEY CONFIRMED RWY 21L. WE SWITCHED TO ANOTHER APCH CTLR. HE TURNED US TO AN INTERCEPT HDG AND ASKED IF WE HAD THE ARPT VISUALLY. WE RESPONDED 'FIELD IN SIGHT.' APCH CLRED US VISUAL APCH; MAINTAIN 4000 FT UNTIL 12 MI OUT; SPD 180 KTS. WE THOUGHT IT WAS ODD THAT WE WERE XING RWY 21R FINAL. IT SOON BECAME APPARENT THAT WE WERE CONVERGING WITH ANOTHER ACFT ON RWY 21L FINAL AND 1000 FT ABOVE US. WE ASKED APCH AGAIN (THIRD TIME) TO CONFIRM RWY 21L. HE (APCH) REPLIED WE WERE CLRED RWY 21R AND SAID; 'I THOUGHT YOU HAD GOT THAT.' WE FLEW BACK TO RWY 21R LOC AND COMPLETED AN UNEVENTFUL APCH AND LNDG. WE HAD BEEN TOLD TO EXPECT RWY 21L TWICE BY APCH. THE FINAL CTLR WAS NOT CLR ABOUT WHICH RWY WE WERE SUPPOSED TO USE. APCH WAS VERY BUSY AND WE WERE RELUCTANT TO ASK AGAIN. WX WAS EXCELLENT SO THERE WAS NO PROB SEEING OTHER ACFT ON FINAL AT DTW.