B767 CAPT EXPEDITED RWY XING AFTER NOTICING ACFT ON TKOF ROLL COMING TOWARD HIM.

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LANDED RWY 22L JFK. CLRED ON TXWY J AND CLRED TO CROSS RWY 22R. AS WE CROSSED TWR REMINDED AN MD80 ON RWY 22R THAT HE WAS TO POS AND HOLD AS HE WAS STARTING TO ROLL. TWR HAD INFORMED US THAT THERE WOULD BE AN ACFT IN POS. WHEN I SAW HIS LIGHTS COME ON I HURRIED TO CLR THE RWY. THE MD80 CLRED THE RWY ON THE TURNOFF SHORTLY AFTER WE CLRED AT THE DEP END. SUPPLEMENTAL INFO FROM ACN 551523: I WAS THE FO ON FLT FROM JFK-DFW ON JUN/SUN/02. WE WERE TAXIING OUT FOR TKOF ON RWY 22R. I TOLD TWR THAT WE WERE READY FOR TKOF IN SEQUENCE AND WE THOUGHT THAT TWR GAVE US A CLRNC TO TAKE OFF RWY 22R; CAUTION WAKE TURB. I READ BACK 'CLRED FOR TKOF ON RWY 22R.' WE COMPLETED THE CHKLIST AS WE TAXIED ONTO THE RWY AND RAN THE ENGS UP FOR TKOF AND STARTED THE ROLL. THE TIME LAPSE WAS ABOUT 1 MIN FROM WHEN I READ BACK THE CLRNC UNTIL WE STARTED TO ROLL. WE SAW A HVY JET TAXI ACROSS THE FAR END OF THE RWY. WE WERE IMMEDIATELY TOLD TO POS AND HOLD WHILE WE WERE ROLLING. WE ABORTED THE TKOF; RECEIVED CLRNC TO TAXI BACK TO THE END OF THE RWY TO GET INTO SEQUENCE AGAIN FOR TKOF.