MULTIPLE RWY OP VISUAL APCHS. ACR X HAD CONFLICT WITH TRAILING Y AFTER 360 DEG TURN.

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BEING VECTORED FOR A VISUAL APCH TO RWY 4R; CTLR POINTED OUT A 727 MOVING THROUGH 12 O'CLOCK. CONFIRMED VISUAL AND WERE INSTRUCTED TO FOLLOW. HANDED OVER TO TWR WHO INQUIRED IF WE HAD THE 727 IN SIGHT OFF OUR L. I RESPONDED THERE WAS A 737 OFF OUR L; THE 727 WAS AHEAD. THE 737 APPEARED TO BE HDG FOR RWY 4L. TWR RESPONDED THAT THE TFC OFF OUR L WAS OUR SEQUENCE. TWR INSTRUCTED US TO FALL IN BEHIND THE 737. I RESPONDED A R 360 DEG TURN WOULD DO IT AND INITIATED THE TURN; NOTING ON THE TCASII THAT A COMPANY SF340 WAS ON THE APCH BEHIND US. THEY HAD BEEN CLRED FOR THE VISUAL TO FOLLOW US TO RWY 4R. PASSING THROUGH 180 DEGS; RA TO DSND WAS ISSUED; HOWEVER; I HAD ESTABLISHED VISUAL WITH COMPANY BY THEN AND MAINTAINED VISUAL THROUGHOUT THE MANEUVER. DURING THIS TIME; TWR MADE SEVERAL CALLS TO COMPANY ACFT WITH NO RESPONSE FROM THEM. ONCE RE-ESTABLISHED ON FINAL; TWR ASKED IF WE HAD COMPANY AT 2 O'CLOCK MOVING R TO L. BY THEN; COMPANY HAD RE-ESTABLISHED ON FINAL AND WAS ACTUALLY AT OUR 11 O'CLOCK. I RESPONDED THAT WE HAD COMPANY IN SIGHT AND WOULD FOLLOW THEM TO RWY 4R. ONCE ON THE GND; I DISCUSSED THE EVENT WITH THE OTHER CREW; WHO CONCURRED WITH OUR VERSION. THEY HAD MAINTAINED VISUAL WITH US THROUGHOUT THE MANEUVER AS WELL. I'M NOT SURE WHERE THE 737 CAME INTO THE PICTURE. I DON'T RECALL HEARING ANY RADIO XMISSIONS UNTIL THE TWR CLRED THEM TO LAND. APCH IDENTED OUR TFC AS A 727 AND THE TWR WAS ALSO UNDER THE IMPRESSION THAT A 727 WAS OUR SEQUENCE; THE ACFT WE WERE IN FACT FOLLOWING. NOT UNTIL I IDENTED THE TFC OFF OUR L AS A 737 WERE WE INSTRUCTED TO FOLLOW THEM. TO THE BEST OF MY KNOWLEDGE; NO RPTS HAVE BEEN FILED.