AN ACR FLC COMPLIED WITH A CLRNC FOR ANOTHER ACFT WITH THE SAME ALPHANUMERICS. OTHER ACFT WAS ON ANOTHER FREQ.

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ACR FLT XAX WAS CRUISING AT FL350 ENRTE BTWN ATL TO SLC. WE WERE LOCATED APPROX 150 NM E OF JNC. THE CAPT WAS THE PF. THE FO HAD LEFT THE COCKPIT TO ATTEND TO PHYSIOLOGICAL NEEDS. I WAS ON OXYGEN AS REQUIRED. ZDV CLRED US TO DSND TO FL310 AT 1500 FPM OR GREATER AND NOT TO EXCEED 270 KTS. THIS CLRNC WAS GIVEN WITH SOME DEGREE OF URGENCY IN THE CTLR'S VOICE. THE SO ANNOUNCED THAT 'HE WOULD RESPOND TO THE RADIO CALL' IN ORDER TO ASSIST THE CAPT WHO WAS ON OXYGEN. HE RESPONDED THAT ACR XAX WAS DSNDING TO FL310. I TOLD HIM THAT DENVER ALSO WANTED 1500 FT OR BETTER AND 270 KTS. HE CALLED CTR AGAIN AND SAID 'ACR XAX DSNDING TO FL310; 270 KTS.' AT THIS TIME THE FO RETURNED TO THE COCKPIT. DENVER CALLED US AND REQUESTED OUR ALT. I RESPONDED THAT WE WERE AT FL335 DSNDING AT 1500 FPM AND 270 KTS AND THAT WE COULD INCREASE THE RATE OF DSCNT IF HE NEEDED IT. HE REPLIED THAT WE HAD TAKEN SOMEONE ELSE'S CLRNC AND TO MAINTAIN FL330; WHICH WE DID. HE THEN REQUESTED THAT WE CLB BACK UP TO FL350. THE COMS THAT SUCCEEDED THIS EVENT INDICATED THAT THE CTLR WAS OPERATING 2 OR MORE FREQS; AND THAT HE WAS INVOLVED IN SOME COM CONFLICTS WITH ANOTHER FLT NUMBERED XAX. WE OBVIOUSLY WERE NOT ON THE SAME FREQ WITH THIS OTHER FLT AND NEVER HEARD ANY RESPONSE FROM THEM. SUPPLEMENTAL INFO FROM ACN 315942: MOST PROBABLY THIS INCIDENT WOULD NOT HAVE OCCURRED IF WE HAD BEEN AWARE OF THE OTHER ACFT WITH THE SAME NUMBERS OR AT LEAST HAD BEEN ON THE SAME FREQ. THERE WAS ADDITIONAL CONFUSION BECAUSE THE CTLR DID NOT ALWAYS USE THE FULL CALL SIGN.