B737 TAXIED AT HIGH SPD BTWN RPTR'S B757 AND THE TERMINAL. COLLISION HAD TO BE AVOIDED BY AGGRESSIVE BRAKING.

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AFTER BEING CLRED TO GATE X AND AT POS (SEE ATTACHED CHARTS) MY FO LOUDLY CALLED OUT 'WHOA; WHOA; WHOA.' GLANCING AT HIM; I SAW THE OBJECT OF HIS ALARM. A CONVERGING B737 WAS TAXIING INSIDE MY STARBOARD SIDE AT A HIGH RATE OF SPD (ESTIMATE ABOVE 20 KTS). I IMMEDIATELY BROUGHT MY ACFT TO A FULL STOP AS THE B737'S WINGTIP CAME DANGEROUSLY CLOSE. THE B737; STILL AT UNREASONABLE SPD PASSED IN FRONT OF ME; ARCED AROUND TO THE R AND SWUNG INTO HIS GATE. WHILE STILL PARKED I QUERIED GND CTLR AS TO 'WHAT HAD JUST HAPPENED.' I COULD NOT BELIEVE WHAT I HAD JUST WITNESSED. APPARENTLY GND CTLR UNAWARE; GAVE ME THEIR LCL PHONE NUMBER. MY ACFT WAS ON THE YELLOW TAXI LINE; APPROX 200 FT INTO THE RAMP WHEN THE INCIDENT OCCURRED; AND HAD THE FO NOT SEEN THE DANGER A COLLISION WOULD HAVE OCCURRED. THERE IS NO ROOM NOR WAS THERE ANY LEGITIMATE REASON FOR THE B737 TO HAVE BEEN IN THE AREA (TAXIED THROUGH VEHICLE LANES AND ALONGSIDE THE B RAMP FLT LINE ACTIVE WITH GND PERSONNEL). I CHKED WITH MY FAIC BEFORE RESUMING TAXI AS MY STOP HAD BEEN FORCEFUL (ALL SEATED; ALL SECURE). DURING DEPLANING; MANY (30-40+) UPSET AND IRATE PAX DEMANDED I 'DO SOMETHING ABOUT THE OTHER ACFT.' MANY COMMENTING 'HOW HE ALMOST HIT US.' SPOKE TO TWR SUPVRS WHO ADVISED OTHER ACFT WAS FLT #XXX. THE FOLLOWING DAY DURING DAYLIGHT HRS; I WAS ABLE TO OBSERVE THE INCIDENT AREA. THAT 2 ACFT HAD BEEN IN THAT RAMP SECTOR WITHOUT COLLIDING HAS TO BE CREDITED TO THE AWARENESS OF MY FO; WITHOUT RESERVATION I CAN SAY HIS ALERTNESS PREVENTED A SERIOUS INCIDENT. IT IS MY CONSIDERED OPINION THAT THE CAPT OF THE B737 OPERATED HIS ACFT IN A RECKLESS MANNER; ENDANGERING THE PAX AND CREWS OF BOTH ACFT.