2 LNDG B737'S ON RWY 36L AT THE SAME TIME IN A NIGHT OP AT TPA; FL.

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WHILE OPERATING AIRLINE FLT XXXX FROM FLL TO TPA; THE CAPT WAS FLYING A VISUAL APCH TO TPA RWY 36L. WE SAW ANOTHER B737 ON THE VISUAL APCH IN FRONT OF US AND ACKNOWLEDGED 'IN SIGHT.' THE OTHER PLANE WAS AT LEAST 5 MI AHEAD AND WAS NOT OF IMMEDIATE SPACING CONCERN. IT LANDED AS WE WERE CONFIGURING BTWN 2000-1500 FT MSL. WE WERE CLRED TO LAND. THE REST OF OUR VISUAL APCH PROCEEDED NORMALLY. THE CAPT LANDED UNEVENTFULLY AND ENGAGED THE THRUST REVERSERS. THEN; AS WE WERE LOOKING DOWN THE RWY; SOME LIGHTS AT THE END OF THE RWY BEGAN MOVING. TO OUR SURPRISE; IT WAS THE OTHER B737 EXITING THE RWY AT TXWY W. IT APPEARS HE WAS STILL ON THE RWY WHEN WE LANDED. I HAD ASSUMED THE ACFT TAXIED OFF OF RWY 36L AT TXWY W6 AND WAS ON THE RAMP SOMEWHERE. I DON'T THINK THE TWR KNEW HE WAS STILL ON THE RWY FOR THE SAME REASON. THE B737 DID NOT HAVE HIS STROBES ON AND WAS THEREFORE HARD TO SEE. I THINK I MIGHT HAVE HEARD TWR TELL HIM TO EXIT AT TXWY W6; BUT I'M NOT SURE. I BELIEVE HE MISSED HIS TURNOFF AT TXWY W6 BECAUSE TXWY W6 HAS SOME CONSTRUCTION ON IT; MAKING THE TXWY APPEAR CLOSED; ESPECIALLY AT NIGHT. THERE WERE TSTMS IN THE AREA; BUT I DON'T BELIEVE THAT CONTRIBUTED TO THE INCIDENT. ALSO; WE WERE ABOUT 1.5 HRS LATE DUE TO A MAINT DELAY AT FLL. I DO NOT THINK THAT WAS A FACTOR EITHER. IN MY OPINION; THE SIGNIFICANT CONTRIBUTING FACTORS TO THIS INCURSION WERE: 1) MY FAILURE TO MONITOR THE PRECEDING ACFT UNTIL HE WAS OFF THE RWY. 2) ACFT MISSING TURNOFF AT TXWY W6. 3) NIGHT. 4) CONSTRUCTION ON TXWY W6. 5) STROBE LIGHT NOT ON WHILE ON ACTIVE RWY; AND 6) TAMPA TWR NOT SEEING THE INCIDENT. TO PREVENT THIS IN THE FUTURE; I WILL MAKE SURE I MONITOR PRECEDING TFC OFF THE RWY.