AN ACR CAPT RPTED THAT; AFTER LNDG AT LAX; HE RECEIVED TAXI INSTRUCTIONS WHICH ULTIMATELY LED TO HIS GATE. AS HE NEARED THE COMPLETION OF THE TAXI; HE WAS TOLD TO CALL THE TWR.

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AFTER LNDG LAX RWY 24R; FLT WAS CLRED TO TAXI EBOUND ON TXWY E AND HOLD SHORT OF TXWY D10. (ULTIMATE DEST WAS GATE XX.) THE REASON FOR THE HOLD SHORT APPEARED TO BE OTHER GND TFC EXITING THE D10 ALLEYWAY. APCHING THE DESIGNATED HOLD SHORT POINT; BOTH THE FO AND MYSELF HEARD THE GND CTLR CLR US TO GIVE WAY TO THE B727 EXITING THE ALLEY ONTO TXWY D (WBOUND); THEN TAXI TO GATE XX. THIS CLRNC WAS ACKNOWLEDGED BY THE FO AND WE CONTINUED TO THE GATE. APCHING THE GATE; WE WERE ADVISED TO PHONE THE TWR AND GIVEN A PHONE NUMBER. AFTER CALLING THE TWR; I WAS INFORMED THAT THE GND CTLR HAD NOT RECALLED THAT HE HAD CLRED US TO THE GATE; AND THOUGHT THAT WE HAD TAXIED WITHOUT CLRNC. I ASSURED THE PERSON ANSWERING THE PHONE THAT WE BOTH WERE POSITIVE THAT WE HAD INDEED RECEIVED AND ACKNOWLEDGED THE CLRNC PRIOR TO PROCEEDING. THE RESPONDER IN THE TWR ALLOWED THAT THE CTLR MAY HAVE HAD A LONG DAY AND FORGOT THAT HE HAD ISSUED THE CLRNC. THE RESPONDER SAID NOT TO WORRY ABOUT THE PROB; AND THAT HE WAS EMBARRASSED THAT WE HAD TO MAKE THE CALL.