LESS THAN STANDARD SEPARATION BETWEEN CORP JET AND ACR. OPERATIONAL ERROR.

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WORKING AUS APCH COMBINED. THERE WERE 8 ACFT UNDER MY CTL--2 TO SATELLITE ARPTS; 3 INBND TO AUS; 1 AUS DEP; 1 MIL DEP OFF BERGSTROM AND 1 RELEASED; 1 VFR OVERFLT. CORP X WAS 12 MI E OF AUS EBND LEVELING AT 10000'. AS I WAS TAKING HDOF ON ACR Y 35 MI E OF AUS I COORDINATED FOR CTL OF Y. AT APPROX THE SAME TIME I RECEIVED HIGHER FOR X. I INSTRUCTED X TO CLB TO 17000'. ACR Y CALLED AND I DSNDED HIM TO 5000' AND EXPEDITE THROUGH 9000' AND GAVE TFC ON CORP Y. AS I WAS ISSUING THIS TFC I SAW X HAD NOT STARTED TO CLB. I TWICE TRIED TO CONTACT X TO GIVE HIM A TURN TO 140 DEGS AND EXPEDITE HIS CLB. AS SOON AS I HEARD NO RESPONSE I TURNED ACR Y RIGHT TO 310 DEGS AND ISSUED TFC ON X AT 11 O'CLOCK; 7 MI AT 10000'. ACR Y WAS DSNDING THROUGH APPROX 10800'. THINKING X MAY HAVE SWITCHED TO ZHU I TRIED TO CONTACT X THROUGH ZHU TO ISSUE A TURN AND TFC. SIMULTANEOUSLY Y HAD APPARENTLY MISSED THE TURN TO 310 DEGS. HE ASKED; 'WHAT WAS THAT HDG?' I RESTATED HDG 310 DEGS AND Y ACKNOWLEDGED. TWICE AGAIN I ATTEMPTED TO CONTACT X--NO REPLY. ACR Y APPEARED VERY SLOW IN TURNING SO I ISSUED A HDG OF 360 DEGS. I THEN TRIED TO GET Y TO VISUALLY SIGHT X BY ISSUING TFC 10 O'CLOCK; 3 MI. Y DID NOT RPT THE TFC; SO I AGAIN ATTEMPTED; THROUGH ZHU; TO TURN X. THEY STATED THEY DIDN'T HAVE HIM. AFTER Y HAD PASSED APPROX 1 MI; X CALLED LEVEL AT 10000'. I ASKED IF HE HAD HEARD MY PREVIOUS XMISSIONS; HE GAVE A CONFUSED REPLY. I SWITCHED X TO ZHU CLBING TO 17000'. NOT HAVING X TO TURN; CLB; OR ISSUE TFC TO WAS PARAMOUNT TO ME--ALSO ACR Y SEEMED SLOW IN RESPONDING TO TURNS. IN HINDSIGHT; IF I HAD ONLY BEEN WORKING RADAR E; WHERE THIS SITUATION TOOK PLACE; I MAY HAVE NOTICED X DID NOT REPLY TO MY INITIAL CLB AND ALSO NOTED X AND Y CLOSURE RATE.