ACR RESPONDS TO TCASII RA AND DSND INTO ACR TFC OPPOSITE DIRECTION. ACR CLBED BACK UP BEFORE LOSS OF SEPARATION OCCURRED.

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ACR X AT FL270 RECEIVED A TCASII RA TO DSND BECAUSE TFC (CGA Y AT FL280) WAS SUPPOSEDLY IN CONFLICT. ACFT WERE SEPARATED BY REQUIRED 1000 VERT SEPARATION. ACR X EXECUTED A DSCNT WHICH IMMEDIATELY PUT HIM IN CONFLICT WITH ACR Z; WHO WAS HEAD-ON AT FL260. MERGING TARGET TFC WAS NOT ISSUED TO EITHER ACFT DUE TO WORKLOAD AT THE TIME. CREW OF ACR X RPTED A 'TCASII RA' AND EXECUTED A DSCNT TO 26700 BEFORE CLBING BACK TO FL270. CREW ALSO RPTED THAT ACR Z (FL260) WAS EVENTUALLY IDENTED BY TCASII. IT IS THE OPINION OF THIS CTLR THAT THIS RA COULD HAVE CREATED A POSSIBLE MIDAIR COLLISION. THIS INCIDENT OR SIMILAR INCIDENTS HAVE OCCURRED BEFORE AT FT WORTH ARTCC. IT APPEARS TCASII DOES NOT IDENT MORE THAN 1 CONFLICT AT A TIME; AND THE ANSWER IS ALWAYS CLB OR DSND WHICH ARE USUALLY THE LAST OPTION USED BY A CTLR. A TURN WILL USUALLY SUFFICE VS UP OR DOWN. ACR X AND ACR Z WERE APPROX 10 MI APART HEAD ON! SUPPLEMENTAL INFO FROM ACN 205811: RECEIVED TFC ALERT ON TCASII SYS DISPLAY SHOWED 1/2 YELLOW BALL AT 12 O'CLOCK POS ON EDGE OF TCASII DISPLAY ALT DATA OF INTRUDER WAS NOT VISIBLE. INTRUDER SYMBOL MOVED FROM 12 O'CLOCK TO 10 O'CLOCK ON EDGE OF DISPLAY AT WHICH POINT IT THEN MOVED DIRECTLY IN TOWARD SUBJECT ACFT SYMBOL OF DISPLAY UNMASKING ALT DATA WHICH INDICATED PLUS 8 (PLUS 800 FT) AND AT THAT INSTANT; A RA 'DSND NOW' SOUNDED AT A DSCNT RATE OF 1800 FPM AND APPEARED ON THE VISUAL DISPLAY. DSCNT WAS BEGUN AT THAT TIME AND ACFT HAD DSNDED 200 FT WHEN 'MONITOR DSCNT' AND WAS SOUNDED. ACFT LEVELED OUT AT 26700 FT AND STARTED CLB BACK TO 27000 FT. SIMULTANEOUSLY AS WE LEVELED AND STARTED A CLB; WE WERE FINALLY ABLE TO ADVISE ATC OF OUR DEV (THE FREQ WAS QUITE BUSY AT THAT TIME) AND THAT WE WERE RETURNING TO OUR ASSIGNED ALT. THE CTLR ADVISED US THAT WE HAD ADDITIONAL TFC AT 12 O'CLOCK AT FL260 AND AS HE WAS XMITTING; WE RECEIVED A SECOND TFC ALERT WITH AN INTRUDER SYMBOL AT 12 O'CLOCK AND ALT DATA INDICATING -7.