ACR X TCASII RA CLB NON ADHERENCE TO ATC INSTRUCTION HAD LTSS FROM ACR Y ALSO TCASII RA CLB. SYS ERROR. EVASIVE ACTION TAKEN.

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ACR X WAS CRUISING AT FL260 TO AVOID TURB. AT VHP VOR WE REQUESTED CLB TO FL310. ZID CLRED US TO CLB AND WE RPTED LEAVING FL260 FOR FL310. PASSING FL272 ATC DIRECTED US TO LEVEL AT FL270. WE RPTED THAT WE WERE ALREADY AT FL275 AND WERE RETURNING TO FL270. AFTER PUSHING THE NOSE OVER TO DSND; WE RECEIVED A TCASII RA 'CLB' COMMAND. WE IMMEDIATELY REVERSED OUR VERT DIRECTION AGAIN TO PUT THE 'NEEDLE IN THE GREEN ARC' WHICH WAS ABOUT 2000 FPM CLB. I THEN LOOKED AT THE RELATIVE POS WHICH WAS INITIALLY AT OUR 9 O'CLOCK POS AND TRIED TO 'VERY QUICKLY' ACQUIRE THE TFC VISUALLY; AFTER ASSURING THAT THE FO; THE ACFT; WAS INDEED AT THE REQUIRED PITCH ALT. THE TCASII RA CHANGED TO AN 'INCREASE CLB' COMMAND. I RETURNED MY ATTN TO THE TCASII TO VERIFY THAT A FURTHER PULL UP WAS ESTABLISHED AND THAT FULL PWR WAS APPLIED. PASSING FL290 WE GOT A 'CLR OF CONFLICT' AND INFORMED ATC THAT WE WERE RETURNING TO OUR CLRED ALT (FL270). SEPARATION HAD BEEN REDUCED. I ASKED ATC WHAT THE OTHER ACFT'S TCASII TOLD HIM TO DO AND AFTER CHKING THEY SAID HE WAS ALSO IN AN RA CLB. THIS DOESN'T MAKE SENSE THAT WE SHOULD BOTH BE CLBING TOWARD EACH OTHER. TO ME WHEN I GOT AN 'INCREASE CLB' COMMAND; AS I UNDERSTAND THE SYS; THAT MEANS THE ACFT OF CONCERN IS DOING SOMETHING ELSE. IT REALLY SEEMED TO ME IF WE COULD HAVE RETURNED TO FL270 AS RESTR THERE PROBABLY WOULDN'T HAVE BEEN A CONFLICT. SUPPLEMENTAL INFO FROM ACN 268010: ACR X WAS WBOUND ON J80 AT FL260 JUST PASSING VHP NBOUND DSNDING TO FL270. X WAS CLBED TO FL310; THEN I AMENDED X TO FL270. Y WAS STOPPED AT FL280. X ADVISED HE WAS AT FL275 AND DSNDING. WAS CLBED TO FL290. NEXT X ADVISED HE HAD A TCASII RA AND HE WAS RESPONDING. THE RA WAS TO CLB AT 2000 FPM. HE CLBED TO FL290. Y ADVISED HE ALSO HAD AN RA AND HE HAD THE TFC IN SIGHT. THEY PASSED WITH 1.5 MI AND 280 FT. WHEN I STOPPED THE X AND Y AT DIFFERENT ALT WE HAD 5.6 MI AND 900 FT THAT DECREASED TO 700 FT AND 4.6 MI. IF X HAD THEN WENT TO FL270 SEPARATION WOULD HAVE BEEN MAINTAINED. WHEN X BEGAN TO CLB IT PUT HIM DANGEROUSLY CLOSE TO Y IN MY OPINION. I FEEL THE TCASII TURNED A CTLED SIT INTO ONE THAT WAS VERY DANGEROUS.