ON ROTATION AT MIA OFF RWY 27R; A G-IV CREW OBSERVE A B727 XING THE RWY AT THE FAR END.

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AFTER BEING CLRED TO TAXI TO RWY 27R AT MIA; WE ARRIVED AT THE TKOF END AND WERE CLRED TO 'HOLD SHORT.' AFTER A COUPLE OF LNDG ACFT; WE WERE CLRED INTO 'POS AND HOLD.' AFTER ABOUT 30 SECS; WE WERE CLRED TO 'TURN RIGHT 290; CLRED FOR TKOF.' THE FO ACKNOWLEDGED 'CLRED FOR TKOF RWY 27R.' AT ABOUT ROTATING SPEED (150 KIAS) I OBSERVED A B727 START ACROSS THE TKOF RWY NEAR THE FAR END. I MADE A SOMEWHAT STEEPER THAN NORMAL INITIAL CLB; RETRACTED THE LNDG GEAR AND CLIMBED OUT STRAIGHT AHEAD PASSING OVER THE ACFT BY ABOUT 200-300 FT. I ASKED THE TWR IF THEY HAD INTENDED TO CLR AN ACFT TO CROSS AHEAD OF US AND THE TWR REPLIED THAT I HAD NOT BEEN CLRED FOR TKOF BUT ONLY INTO POS AND HOLD. I REPLIED THAT WE HAD BEEN CLRED FOR TKOF AND HAD ACKNOWLEDGED THE CLRNC. WE WERE TOLD TO TURN TO HEADING 290 AND CONTACT DEP. AFTER ABOUT 20 MINS OF FLT TIME; WE WERE ASKED TO CONTACT MIA APCH CTL BY TELEPHONE. I SPOKE WITH THE TWR SUPVR WHO SAID THEY HAD REPLAYED THE TAPE AND; IN FACT; WE HAD BEEN CLRED FOR TKOF. HOWEVER; THE TWR OPERATOR; IN ERROR; HAD IMMEDIATELY AFTER CLRING US FOR TKOF; CLRED ANOTHER ACFT TO CROSS THE RWY. AFTER SOME DISCUSSION; I TOLD THE SUPVR THAT I DID NOT INTEND TO TAKE ANY FURTHER ACTION OTHER THEN TO FILE A NASA; ASRS RPT. ATC AT BUSY ARPTS LIKE MIA ARE ALWAYS UNDER TREMENDOUS PRESSURE TO KEEP TFC MOVING AT THE FASTEST RATES CONSISTENT WITH SAFETY. THE CHK AND BALANCE IS THAT THEY HAVE POSITIVE CTL RULES ABOUT WHEN AN ACFT CAN BE SAFELY CLRED TO CROSS A RWY AFTER A DEPARTING ACFT. CROSSING ACFT ALSO HAVE A RESPONSIBILITY TO LOOK BOTH WAYS PRIOR TO XING AN ACTIVE RWY. NEITHER OF THESE SAFETY PRECAUTIONS WORKED IN THIS CASE. WE WERE FORTUNATE OUR ACFT HAD THE PERFORMANCE TO ROTATE AND CLB SUFFICIENTLY TO CLR THE XING B727 BY A PRETTY LARGE MARGIN. I DON'T HAVE A DEFINITIVE RECOMMENDATION TO PREVENT SIMILAR RWY INCURSION EVENTS IN THE FUTURE OTHER THAN TO REEMPHASIZE STICKING TO THE SAFETY CHKS AND BALANCES STATED ABOVE. I DOUBT THAT DEVICES SUCH AS GATES OR LIGHTS WOULD HAVE PREVENTED THIS INCIDENT SINCE HUMAN INTERVENTION IS STILL REQUIRED TO ACTIVATE THE GATE OR LIGHT AND THAT HUMAN OVERRIDE DID NOT WORK IN THIS CASE.