ARTCC RADAR CTLR CLBED A CPR JET THROUGH AN ALT OCCUPIED BY AN ACR JET. THE ARTCC D CTLR SAW THE POTENTIAL CONFLICT LTSS ABOUT TO OCCUR AND WARNED THE RADAR CTLR. THE RADAR CTLR DSNDED THE CPR JET AND GAVE BOTH ACFT TA'S AND STANDARD SEPARATION WAS LOST. THE CONFLICT ALERT DID NOT ACTIVATE AND RPTR INDICATES THAT APPARENTLY NEITHER ACFT INVOLVED HAD TCASII.

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TOOK RADAR HDOF ON ACFT #1. ACFT #1 WAS A DEP FROM ADJACENT CTR. SINCE IT WAS A DEP; OUR LOA INDICATES THOSE ACFT WILL BE CLBING TO FL260. ADJACENT CTR CALLED ME AFTER I HAD THE HDOF; THAT ACFT #1 WAS CLBING TO FL310. I APPROVED IT; SINCE ACFT #1 WAS REQUESTING FL390. ACFT #2 WAS IN LEVEL FLT; OPPOSITE DIRECTION AT FL330. I WAS CONCERNED ABOUT GETTING ACFT #1 UP TO REQUESTED ALT BECAUSE THERE WAS ANOTHER ACFT AT FL310; SAME DIRECTION AS ACFT #1; BEHIND ACFT #1. I DID NOT HAVE THE HDOF ON THAT ACFT YET; SO I COULDN'T TELL HOW FAST IT WAS IN RELATION TO ACFT #1. I DID A TFC SEARCH IN MY SECTOR WHERE MOST OF THE CONFLICTIONS TAKE PLACE FOR ACFT 1'S RTE OF FLT. I FAILED TO OBSERVE ACFT #2'S RELATIVE POS. I ASSIGNED ACFT #1 FL390 AND IMMEDIATELY NOTICE ANOTHER ACFT CLOSE TO MY BOUNDARY THAT WAS HEAD ON WITH 2 OTHER AIRPLANES I WAS WORKING. I CALLED THAT SECTOR AND ASKED WHAT WAS GOING ON WITH SAID ACFT. CTLR SAID HE WAS NOT YET IN COMS WITH ACFT AND HE DIDN'T KNOW WHY THAT ACFT WAS OFF HIS COURSE. I THEN TURNED 1 OF THE 2 ACFT AWAY FROM THE INTRUDER ACFT. RIGHT AFTER THAT; MY D-SIDE (MANUAL CTLR) ALERTED ME TO THE HEAD-ON SIT BTWN ACFT #1 AND ACFT #2. AT THAT POINT THEY WERE LESS THAN 10 MI APART AND ACFT #1 MODE C INDICATED FL317. I TOLD ACFT #1 TO 'DSND AND MAINTAIN FL290; EXPEDITE DSCNT; TA 12 O'CLOCK; 5 MI; FL330.' I THEN TOLD ACFT #2 'TA; TFC 12 O'CLOCK; 1 MI; FL317 DSNDING.' I NEXT TOLD ACFT #1 TO RPT LEAVING FL310. THIS HAPPENED SO QUICK (SINCE IT WAS HEAD- ON). MY MILEAGE GIVEN IN TFC CALLS WAS PROBABLY NOT PRECISE; BUT AT LESS THAN 10 MI HEAD-ON; IT'S IMPOSSIBLE TO TELL. I SHOULD HAVE TOLD AFCT #1 TO 'DSND IMMEDIATELY' AS PER 7110.65 ATP. ALSO; IT SHOULD HAVE BEEN 'SAFETY' ALERT; NOT TA. ACFT #1 WAS A CPR JET; NO TCASII. ACFT #2 WAS A FOREIGN CARRIER; SO I DO NOT BELIEVE IT HAD TCASII EITHER. THIS SIT WAS TRAUMATIC FOR ME AND ONLY REINFORCES MY BELIEF THAT 2 SETS OF EYES ARE BETTER THAN 1. I HOPE THE FAA WILL QUIT BEING SO CONCERNED WITH HOW MUCH IT COSTS TO GET ADEQUATE STAFFING. I AM SO LUCKY I HAD AN ALERT D-SIDE PLUGGED IN WITH ME. IF HE HADN'T; THOSE 2 ACFT MIGHT HAVE BEEN A LOT CLOSER THAN 1300 FT. ALSO; THE CONFLICT ALERT FUNCTION NEVER ACTIVATED. CONTRIBUTING FACTOR THAT I DIDN'T CATCH MY MISTAKE WAS ADJACENT FACILITY'S DEVIATING ACFT THAT CONSUMED MY ATTN.