ALTDEV ALT OVERSHOT - ACR CREW RELIED ON THE B737-300'S FMC/VNAV TO LEVEL OFF FROM A STEEP DSCNT (STARTED DOWN LATE BECAUSE OF CTR) AND IT FAILED TO DO SO.

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WE WERE DSNDING TO 11000 FT AT BRIDGE INTXN. BECAUSE OF EARLIER TFC CONFLICTS CLRNC WAS LATE AND WE HAD A HIGH RATE OF DSCNT. THE ACFT WAS ON AUTOPLT; LNAV AND VNAV. WE HAD BEEN POINTED OUT TFC; THE DH-8; EARLIER AT 10000 FT OUR 3 O'CLOCK. WE GOT A TCASII ALERT AND AN 'RA' 'DECREASE VERT SPD' AS WE WERE APCHING 11000 FT WE AT FIRST MONITORED OUR PERFORMANCE AND WHEN WE REALIZED WE WERE GOING TO BUST 11000 FT BOTH CAPT (PNF) AND FO (PF) APPLIED BACK PRESSURE TO LEVEL OFF. WE LEVELED OFF MAYBE 10800 FT AND RETURNED TO 11000 FT DURING THIS TIME THE DH-8 HAD MOVED TO OUR 10 O'CLOCK POS PASSING UNDER US. DURING SUBSEQUENT LEVEL OFF; SPD REDUCTION; RETRIMMING; FO ALLOWED ACFT TO DSND BACK TO 10700 FT BEFORE REENGAGING AUTOPLT AND LEVELING AGAIN AT 11000 FT. DURING THE TIME WE WERE REACTING TO THE 'RA' ATC ASKED IF WE STILL HAD THE DASH 8 AND WERE LEVEL AT 11000 FT. ATC WAS THEN VECTORING BOTH OF US TO THE SAME RWY 36L; BUT HAD ISSUED NO SPD CTL SO FOR SEVERAL MI WE WERE DIRECTLY OVER THE DH-8 AND RAPIDLY APCHING THE POINT OF DSCNT. ATC FINALLY SPLIT US AND SENT THE DH-8 TO RWY 36R. I HAVE 5000 HRS IN B-737 - 300/400 AND I DO NOT UNDERSTAND WHY THIS TIME WE OVERSHOT OUR ALT WITH LNAV AND VNAV AND THE CORRECT ALT SELECTED.