MD-11 CREW AND OTHER ACR HAD SIMILAR CALL SIGNS. THE CTLR MAY HAVE MIXED UP THE ACFT AND DID NOT CATCH THE ERROR ON HEARBACK.

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3 MEMBER CREW OF MD-11 WAS IN LAST FEW MINS OF AN 11 HR 30 MIN CREW DAY ENRTE HONG KONG TO ANCHORAGE. BACK SIDE OF THE CLOCK EVOLUTION. WHILE BEING VECTORED IN THE TERMINAL AREA IN IMC CONDITIONS ON FREQ 135.150 BY ANCHORAGE APCH CTL; CREW RECEIVED INSTRUCTIONS TO TURN TO HDG 040 DEGS; DSND TO 3000 FT FROM 6000 FT; AND INTERCEPT THE RWY 6 LOC AT ANC. CREW READ CLRNC BACK PROPERLY; RESPONDING 'ACR X. HVY;' AND BEGAN COMPLYING. VERY SHORTLY AFTERWARD' CTLR ADVISED WE HAD APPARENTLY ACCEPTED INSTRUCTIONS FOR ANOTHER ACFT. CTLR GAVE US REVISED INSTRUCTIONS WITH WHICH WE COMPLIED. SOME MINS; LATER; CTLR SAID ACR X SORRY ABOUT THE MIX-UP BACK THERE; AND THAT HE WISHED HE HAD CAUGHT OUR READBACK. CTLR THEN VECTORED US TO ILS RWY 6 FINAL AND TURNED US OVER TO TWR FREQ FOR AN UNEVENTFUL LNDG. AT NO TIME WAS LOSS OF SEPARATION A FACTOR. ACR Y HVY WAS ON OUR FREQ AT THE SAME TIME AND NEAR OUR VICINITY ON VECTORS TO ANCHORAGE; AND AFTER CORRECTING OUR ACFT; CTLR REISSUED SIMILAR CLRNC TO ACR Y. AT NO TIME DID ACR Y EVER ANSWER THE ORIGINAL CLRNC UNTIL REISSUED BY ANC APCH. WE NEVER DSNDED FROM 6000 FT.