A B737-300 FLC ACCEPTS A CLRNC MEANT FOR ANOTHER FLT WITH A SIMILAR SOUNDING CALL SIGN WITH CTLR INTERVENING TO STOP THEIR DSCNT W OF MOHAK INTXN NEAR TUS; AZ.

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AT FL370 ENRTE FROM LAX TO TUS WE CHKED IN WITH ZLA (HI) AND HE INFORMED US (ACR X ABC) TO USE CAUTION BECAUSE THERE WAS A SIMILAR SOUNDING CALLSIGN (ACR X BC) ON THE FREQ. AFTER A FEW ROUTINE TFC CALLS FROM CTR; THE CTLR ISSUED A CLRNC TO CROSS MOHAK INTXN AT FL250. THE CAPT AND I BOTH HEARD 'ACR X ABC.' THE CAPT ACKNOWLEDGED AND CLRLY READ BACK THE CLRNC. SINCE MOHAK WAS ON OUR RTE OF FLT AND WITHIN REASONABLE RANGE OF OUR DEST; THE CLRNC MADE PERFECT SENSE. THE CAPT ROLLED FL250 INTO OUR MCP ALT WINDOW AND WHEN WE INTERCEPTED THE DSCNT PROFILE TO MAKE THE XING RESTR; I DSNDED US OUT OF FL370. PASSING APPROX FL362 (1200-1500 FPM) THE CTLR TOLD US TO MAINTAIN FL370. I IMMEDIATELY STOPPED THE DSCNT AND BEGAN A CLB BACK TO FL370 WHILE THE CAPT QUERIED THE CTLR ON OUR XING RESTR AT MOHAK. THE CTLR INFORMED US THAT THE XING RESTR HAD BEEN GIVEN TO 'ACR X BC' AND THAT HE HAD TOLD US AT THE TIME THE CLRNC WAS GIVEN (TO ACR X BC) TO MAINTAIN FL370. HE ALSO INFORMED US THAT THERE WAS TFC BELOW US. OUR TCASII DISPLAYED TFC APPROX 7 NM BEHIND US AT FL330. WE CONTINUED TO TUS WITHOUT FURTHER INCIDENT. SINCE BOTH THE CAPT AND I WERE VERY AWARE THAT ACR X BC WAS ON THE FREQ; WE WERE BOTH HIGHLY VIGILANT TO THE POTENTIAL CALLSIGN MIX-UP. THERE WERE NO DISTRS IN THE COCKPIT (IE; FLT ATTENDANTS; DEEP CONVERSATION; ETC); WE WERE BOTH LISTENING CLOSELY TO THE RADIO. IT BECAME OBVIOUSLY THAT BOTH ACR X BC AND WE READ BACK THE CLRNC AT THE SAME TIME. WE NEVER ACKNOWLEDGED OR READ BACK ZLA'S INSTRUCTIONS TO MAINTAIN FL370 AFTER WE ACKNOWLEDGED THE MOHAK XING RESTR. 2 THINGS THAT COULD HAVE PREVENTED THIS ALTDEV COME TO MIND: 1) IF WE HAD RPTED LEAVING FL370 (TO MAKE THE MOHAK XING RESTR; AND 2) IF THE CTLR HAD PRESSED US FOR AN ACKNOWLEDGEMENT AFTER HE TOLD US TO MAINTAIN FL370. ALSO; THERE MUST BE SOME STANDARD WAY FOR A CTLING AGENCY TO TEMPORARILY CHANGE A CALL SIGN FOR ONE OF THE ACFT WHEN CALLSIGNS THIS SIMILAR ARE ON THE SAME FREQ AND/OR RTE. SUPPLEMENTAL INFO FROM ACN 518167: ONLY THE TAPES WILL TELL WHETHER WE MISHEARD THE ORIGINAL CLRNC (WE ARE SURE WE DID NOT; OF COURSE). WHAT IS CLR IS THAT BOTH ACR X ABC AND ACR X BC FLTS BOTH ACKNOWLEDGED THE CLRNC. DUE TO THE NATURE OF THE RADIOS; THE ONLY ONE TO NOTICE IF BOTH ACFT ACKNOWLEDGE THE CLRNC IS THE RECEIVER; IN THIS CASE ATC. ONCE AGAIN; WITH SIMILAR CALL SIGNS ALL PARTIES NEED TO USE CAUTION.