A SYS ERROR OCCURS WHEN SIMILAR SOUNDING FLT NUMBERS ARE MIXED UP IN A DSCNT CLRNC AND THE RADAR CTLR RELIEVED OF HIS POS AT ZAB; NM.

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WE WERE LEVEL AT FL390 WHEN ATC INSTRUCTED US TO DSND TO FL350. IN THE DSCNT; ATC SAID 'ACR X; CONTINUE DSCNT TO FL310 AND KEEP THE SPD UP WHEN YOU LEVEL OFF.' I ANSWERED THE CLRNC AND WE CONTINUED DOWN. SOMEWHERE AROUND FL334 OR SO; ATC ASKED US OUR ALT. I RESPONDED WITH OUR CURRENT ALT AND SAID WE WERE DSNDING DOWN TO FL310. ATC TOLD US TO TURN R TO 300 DEGS AND CLB TO FL350. HE THEN TOLD THE OTHER ACR ACFT TO MAKE A R TURN IMMEDIATELY. I TOLD THE CTLR WE WERE CLBING TO FL350 AND THAT WE HAD BEEN CLRED TO FL310. THERE WAS NO RESPONSE. THE NEXT TIME WE HEARD ATC TALK; IT WAS A DIFFERENT CTLR. THE ACR Y ACFT SAID HE HAD AN A. WE ALSO HAD AN RA TO CLB. I REMEMBER SEEING A 400 FT DIFFERENCE ON THE TCAS BTWN US AND THE OTHER ACFT. I LOOKED OUT THE WINDOW AND COULD SEE THE OTHER ACFT AT ABOUT OUR 10 O'CLOCK POS AND ABOUT 1-2 MI HORIZ DISTANCE. I THINK THE PROB COULD HAVE BEEN THE FACT THAT THERE WAS A THIRD ACR WITH SIMILAR ALPHA NUMERIC ON THE FREQ IN FRONT OF US ON HIS WAY TO PHX ALSO. I THINK THE CTLR MIGHT HAVE BEEN WANTING OUR CLRNC TO FL310 TO BE FOR THE THIRD ACFT. THE CTLR NEVER SAID WE WERE IN THE WRONG AND NEVER GAVE US A NUMBER TO CONTACT.