AN ACR L1011 LANDED RWY 9R AND SAID THAT THE TWR CLRED THEM TO CROSS RWY 9L DURING THEIR LNDG ROLLOUT. ANOTHER ACR L1011 WAS CLRED FOR TKOF ON RWY 9L AND TWR HAD THEM ABORT THEIR TKOF DUE TO THE OTHER L1011 XING THE RWY DOWNFIELD. TWR CTLR TOLD THE FIRST L1011 THAT HE HAD BEEN TOLD TO HOLD SHORT. GND CTLR HAD THE FIRST L1011 CONTACT THE TWR AFTER PARKING.

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ACFT #1 LANDED ON RWY 9R AT ATL. DURING ROLLOUT ATL TWR INSTRUCTED ACFT #1 THAT IT WAS CLRED TO CROSS RWY 9L. ACFT #1 ACKNOWLEDGED WITH CALL SIGN AND REPEATED 'CLRED TO CROSS RWY 9L.' AS ACFT #1 WAS XING RWY 9L; TWR MADE A XMISSION TO ACFT #2 THAT 'TKOF CLRNC IS CANCELED.' ACFT #2 DISCONTINUED ITS TKOF. THE TWR THEN TOLD ACFT #1 IT HAD BEEN INSTRUCTED TO HOLD SHORT OF RWY 9L. ACFT #1 RESPONDED THAT ACFT #1 HAD BEEN CLRED TO CROSS RWY 9L AND HAD ACKNOWLEDGED THE SAME. ACFT #1 CONTACTED GND CTL AND WAS INSTRUCTED TO CALL THE TWR VIA PHONE LINE. TAXI TO THE GATE PROCEEDED WITHOUT FURTHER INCIDENT. AT NO TIME DID ACFT #1 AND ACFT #2 COME IN CLOSE PROX TO EACH OTHER. SUPPLEMENTAL INFO FROM ACN 349743: AS WE WERE TAXIING INTO POS; I WAS RUNNING BEFORE TKOF CHKLISTS BOTH VERBAL AND SILENT. I DIDN'T HEAR TWR GIVE US TKOF CLRNC. I ASKED THE CAPT AND FO WHO SAID WE RECEIVED IT. I THOUGHT I HEARD TWR GIVE ANOTHER ACFT CLRNC TO CROSS THE RWY. AS CAPT STARTED TO ADD TKOF PWR; I NOTICED AN L1011 ABOUT 3/4 OF THE WAY DOWN THE RWY START TO CROSS. I CALLED OUT 'ACFT ON RWY' TWICE IN CLOSE SUCCESSION. ON THE SECOND CALL; THE CAPT ABORTED. I BELIEVE THE CAPT AND FO WERE CONCENTRATING ON SPINNING UP THE ENGS AND DIDN'T NOTICE THE OTHER ACFT INITIALLY. WE NEVER GOT CLOSE TO FULL PWR WHEN WE ABORTED. I ESTIMATE OUR AIRSPD WAS 20-25 KTS WHEN WE ABORTED. IN A BRIEF DISCUSSION WITH TWR AFTERWARDS; IT APPEARED THAT WE WERE CLRED FOR TKOF AND THE OTHER ACFT WAS CLRED TO TAXI ACROSS OUR RWY AFTER LNDG ON PARALLEL RWY. (SAME TWR FREQ FOR BOTH RWYS.) I FAILED TO MENTION THAT AS WE WERE BEING CLRED ONTO RWY; TWR CLRED 2 ACFT TO CROSS DOWNFIELD. THEN I BELIEVE WE WERE CLRED FOR TKOF AND THEN OTHER ACFT CLRED TO CROSS IN FRONT OF US. A FACTOR MAY HAVE BEEN CREWS IN BOTH ACFT LISTENING MORE INTENTLY FOR THEIR OWN CLRNC AND NOT PAYING VERY CLOSE ATTN TO OTHER CLRNCS.