FLC OF AN ACR WDB SIGHTED ANOTHER WDB CONVERGING AT THE SAME HIGH CRUISE ALT AND WAS SUBSEQUENTLY GIVEN A HIGHER ALT. AT APPROX THE SAME TIME; THE ACFT TCASII GAVE AN RA TO DSND WHICH WAS NOT RESPONDED TO SINCE THE OTHER ACFT WAS IN SIGHT.

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I SAW ACFT AT MY 12:30 TO 1:00 O'CLOCK POS. I VERIFIED ITS ALT AS BEING (TCASII) FL370; THE SAME AS MY OWN. I CALLED WINNIPEG CTR AND SAID 'ARE YOU AWARE THAT I HAVE AN ACFT AT MY 12:30 POS FL370 AND CONVERGING?' REPLY FROM WINNIPEG 'CLB TO 390!' THE FO SET THE NEW ALT AND I HIT THE FLT LEVEL CHANGE BUTTON FOR EXPEDITED CLB. WE THEN GOT THE TA AND ONCE ESTABLISHED IN THE CLB WE RECEIVED RA TO DSND. SINCE I HAD THE ACFT IN SIGHT THE ENTIRE TIME I DID NOT THINK IT WOULD BE WISE TO DECREASE SEPARATION BY FOLLOWING THE TCASII RA COMMAND. TO KEEP THINGS SIMPLE; WE WERE ABOVE THE INTRUDER ACFT AT 37500 FT AND CLBING WHEN WE RECEIVED THE RA TO DSND -- NO WAY! I FOLLOWED THE ATC CLRNC AND CLBED TO FL390 THE RA STOPPED -- AND THE CTLR DIDN'T SAY A WORD. IT WAS VERY QUIET ON THE FREQ. IT IS MY BELIEF THAT IF IT WERE NOT VFR TODAY AND I DID NOT SEE THAT OTHER ACFT 2 747'S WOULD HAVE COLLIDED TODAY AND IN ADDITION TCASII FAILED BY GIVING ME A DSND COMMAND INSTEAD OF TELLING ME TO CLB. I BELIEVE THIS WAS AN ATC CTLR FAILURE AS BOTH ACFT WERE IN RADAR CONTACT.