RWY INCURSION AND A NEAR GND CONFLICT WHEN AN MD80 ON ROLLOUT RWY 24R; TXWY AA TURN OFF; AND A B737 LNDG RWY 24L CREATES A POTENTIAL TFC CONFLICT; AS LAX TWR CTLR CHANGES HIS MIND NECESSITATING A GAR.

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LANDED RWY 24R BEHIND ACFT Y. ACFT Y WAS HOLDING SHORT RWY 24L AT TXWY AA. ACR Z WAS CLRED TO CROSS RWY 24L AS WE EXITED RWY 24R AT TXWY AA. I INQUIRED IF WE COULD KEEP IT ROLLING. LAX TWR GAVE CLRNC; 'ACFT X CLRED TO CROSS RWY 24L' I ACKNOWLEDGED THE CLRNC. ONCE I TERMINATED THE XMISSION; IT WAS OBVIOUS THE CTLR HAD BEEN TALKING WHILE I WAS TALKING. I HEARD SOMETHING LIKE '...SHORT.' IMMEDIATELY TWR CAME BACK AND TOLD US TO HOLD SHORT OF RWY 24L. I ACKNOWLEDGED THIS NEW CLRNC AND A B737 (Z) WAS TOLD TO GO AROUND. WE HAD CROSSED THE HOLD SHORT LINE; BUT DID NOT CROSS THE LINE DELINEATING THE RWY. A SUBSEQUENT CLRNC TO CROSS WAS ISSUED AND WE PROCEEDED TO THE GATE UNEVENTFULLY. CAPT CONTACTED THE TWR VIA PHONE. THE CTLR SAID THAT THEY ACKNOWLEDGED THAT WE WERE GIVEN A CLRNC TO CROSS; BUT SUBSEQUENTLY RESCINDED IT. THEY SAID THEY SAW WE WERE NOT STOPPING AND ISSUED THE HOLD SHORT AGAIN; WHILE ORDERING B737 TO GO AROUND. WE SAID WE BELIEVED THAT I WAS READING BACK THE ORIGINAL CLRNC AS THEY WERE ISSUING THE FIRST 'HOLD SHORT' CLRNC; THEREBY BLOCKING THE XMISSION. THEY SAID THAT SINCE THE B737 WENT AROUND; THERE WAS NO INCURSION AND SEPARATION WAS NOT A PROB.