FOREIGN CARRIER WITH SIMILAR IDENTS STEPPED ON EACH OTHER'S CLRNC; XXX TOOK CLRNC MEANT FOR XXY.

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I WAS IN THE R SEAT PERFORMING IOE TRAINING FOR FOREIGN XXX CARRIER. OUR ACFT WAS HDG S TO LAX ON A FLT FROM ANCHORAGE. THE CURRENT CLRNC WAS DIRECT LAX FROM TOU VOR IN WASHINGTON AT FL370. OAKLAND CENTER WAS ALSO WORKING ANOTHER CARRIER FOREIGN XXY AT THE SAME TIME. OAKLAND CENTER INSTRUCTED XXX TO COME UP ON THE SAME FREQ THAT WAS CTLING XXY. AFTER SWITCHING TO THE NEW FREQ; THE XXX RADIO OPERATOR INITIATED CONTACT AT THE SAME TIME ATC WAS ISSUING A DSCNT CLRNC TO XXY TO DSND TO 350. THE XXX RADIO OPERATOR BLOCKED PART OF XXY CLRNC AND THEY HEARD 'XX DSND TO FL350.' THE XXX CAPT STARTED A DSCNT AND THE RADIO OPERATOR CALLED DEPARTING FL370 FOR FL350. OAKLAND CALLED BACK THAT THE CLRNC WAS FOR XXY; ANOTHER ACFT; AND THAT XXX WAS TO MAINTAIN FL370. XXX IMMEDIATELY CLBED BACK TO FL370 WITH AN EXCURSION OF 1000 FT. THE PRIMARY CAUSE OF THIS DEV WAS XXX RADIO OPERATOR NOT LISTENING ON FREQ BEFORE SPEAKING TO ASSURE THAT THE FREQ IS CLR. ANOTHER ELEMENT ADDING TO THE CONFUSION IS THERE ARE AT LEAST 3 AIRLINES WITH 'XX' IN THEIR CALL SIGN: XXX FROM SHANGHAI; XXY AIRLINES FROM TAIWAN; AND ZXX FROM BEIJING.