ACR X UNAUTH DSCNT FROM ASSIGNED ALT TCASII RA HAD LTSS FROM ACR Y.

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I WAS WORKING THE EBOUND DEP FROM DFW. I HAD AN ACR X AT FL220 XING MY SECTOR. ACR Y WAS CLBING EBOUND TO FL210. I CALLED TFC TO THE CLBING ACFT ABOUT THE B727 AT FL220 AND REISSUED FL210. HE (A B757) SAID HE HAD THE B727 ON TCASII. I WENT TO CALL TFC TO THE B727 ABOUT THE CLBING B757 AND SAW THAT HIS ALT SHOWED FL217 AND DSNDING. I ASKED THE B727 TO VERIFY LEVEL FL220 AND GOT NO RESPONSE. I TRIED AGAIN STILL WITH NO RESPONSE. THE B757 SAYS HE IS GETTING AN RA AND SAYS THAT HE IS CLBING. THE B727 FINALLY CALLS AND SAYS THAT HE GOT AN RA AND IS DSNDING TO GET AWAY FROM TFC AT HIS ALT. IF THESE 2 ACFT WOULD HAVE LISTENED TO ME INSTEAD OF A PIECE OF MACHINERY THEY WOULD HAVE BEEN PROPERLY SEPARATED BY 1000 FT. INSTEAD THEY TRIED TO SEPARATE THEMSELVES AND ALMOST HAD A MIDAIR COLLISION. THE CLOSEST POINT WAS 1.3 MI AND 300 FT. TCASII IN THE ENRTE ENVIRONMENT IS A BAD ACCIDENT WAITING TO HAPPEN. UNTIL THEY CAN MODIFY THIS EQUIP SO EACH AIRPLANE'S COMPUTER KNOWS WHAT THE OTHER IS DOING; TCASII WILL NEVER WORK. I DON'T THINK I HAVE EVER HEARD OF A CTLR CLBING AN ACFT INTO ANOTHER AND THE 2 HIT YET WE HEAR MONTHLY HOW 2 ACFT HAVE GOTTEN RA'S TO CLB AND DSND AND ALMOST HIT.