ALTDEV ALT EXCURSION WHEN FLC RECEIVES A TCASII RA ON OPPOSITE DIRECTION TFC.

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WHILE ENRTE LEVEL AT FL290 WERE GIVEN A FREQ CHANGE (HDOF). BEFORE NEW FREQ WAS SELECTED WE RECEIVED A TA 'TFC; TFC' FROM TCASII. TARGET WAS 12 O'CLOCK; 5 MI; MAX RANGE OF DISPLAY. ALMOST IMMEDIATELY THEREAFTER; RECEIVED RA 'CLB; CLB.' TFC WAS IN SIGHT; CLOSING. TCASII SHOWED TFC 1000 FT -- THAT IS; 1000 FT BELOW. I DISENGAGED AUTOPLT AND STARTED A SLOW CLB. TCASII THEN ANNUNCIATED 'MONITOR VERT SPD.' WE CLBED APPROX 500 FT OVER ASSIGNED ALT OF FL290 AS TFC PASSED CLR. DSNDED BACK TO FL290 AND CHKED IN WITH THE NEW CTLR. AFTER RPTING LEVEL; WE EXPLAINED THE BRIEF ALT CHANGE. CTLR SAID HE OBSERVED CLB AND ASKED IF THE TCASII WARNING WAS CAUSED BY THE TFC 1000 FT BELOW WHICH HAD JUST PASSED. I SAID THAT MUST HAVE BEEN THE CAUSE. AFTER THE TFC PASSED; TCASII ANNUNCIATED; 'CLR OF CONFLICT;' BUT THERE NEVER WAS A CONFLICT. ALTHOUGH WE HAD TFC IN SIGHT; ALT OF OTHER ACFT AT ALT AND HIGH CLOSURE RATES; IS HARD TO JUDGE VISUALLY AND I DECIDED A SMALL CLB TO COMPLY WITH TCASII WAS SAFEST. THE TCASII WORKED FINE THROUGHOUT REMAINDER OF FLT; BUT WE WROTE IT UP FOR MAINT.