LESS THAN STANDARD SEPARATION BETWEEN 2 ACR. OPERATIONAL ERROR.

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WE; ACR X; WERE INBND TO DFW. WE HAD JUST PASSED ARDMORE VOR SBND WHEN DIRECTED TO DSND FROM FL280 TO FL240 AND MAINTAIN 280 KTS IAS. WE ACKNOWLEDGED THE XMISSION AND PROCEEDED AS CLRED. AFTER WE LEVELED AT FL240 WE RECEIVED A XMISSION TO TURN IMMEDIATELY 90 DEGS RIGHT; AND WE DID SO. AFTER WE ACKNOWLEDGED THE COMMAND WE HEARD ACR Y SAY HE HAD US IN SIGHT AND WAS ALSO TURNING. AFTER THE CTLR SPOKE WITH ACR Y HE CAME BACK TO US; ACR X; AND ADVISED US WE WERE TO BE AT FL250 AND NOT FL240. WE RESPONDED BY STATING WE HAD RECEIVED CLRNC TO DSND TO FL240 AND MAINTAIN 250 KTS. ACR Y SAID THIS WAS TOO CLOSE AND WE NEEDED TO DISCUSS THIS FURTHER. WE; X CREW; NEVER HAD Y IN SIGHT AND HIS DIRECTION WAS UNKNOWN TO US. POS AND DIRECTION OF X WAS FL240; 280 KIAS; 198 DEG R ADM/BPR 018 DEG R; CORRECT ALT FOR DIRECTION BEING FLOWN. AFTER THE INCIDENT ACR Y RECEIVED CLRNC TO DSND TO FL230. SUPPLEMENTAL INFO FROM ACN 96297: SHORTLY AFTER REACHING FL240 CTLR URGENTLY RECLRED US; ACR Y TO FL230. AT OUR 10 O'CLOCK POS WAS ACR X AT SAME ALT IN A SHARP RIGHT TURN. ESTIMATED DISTANCE 2 MI OR LESS AT SAME ALT. THE SNITCH COMPUTER PROGRAM HAD ALERTED CTLR TO CONFLICT AT THE TIME THE OTHER ACFT WAS IN A BLIND SPOT TO ME DUE TO WINDSHIELD POST.