TCASII. INTRUDER TFC RPTED BY ATC AND FLC HAD IT VISUALLY; BUT THE TFC WAS DSNDING AND RPTR SAID IT DSNDED BELOW THEIR ALT WHEN SUDDENLY IT STARTED A CLB. RPTR WAS CONFUSED WHY THE TFC STARTED A CLB OUT OF A DSCNT. TFC WAS NEVER CLOSER THAN 2 MI.

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ATC ADVISED US OF JET TFC ON A DSCNT TO DLG. I REPLIED AND TOLD THEM TO KEEP US ADVISED OF THEIR POS. ATC ADVISED US AGAIN OF THE JET'S POS AT THE SAME TIME THE TFC SHOWED UP ON OUR TCASII (15 MI). AT THAT TIME I TURNED ON THE LNDG LIGHTS AND ADVISED MY FO TO LOOK FOR THE TFC. AT 6 MI ON THE TCASII; MY FO SPOTTED TFC AT 11:30 O'CLOCK AND SLIGHTLY HIGHER. AT THAT TIME I SAW THE TFC ALSO AND ADVISED ATC THAT WE HAD TFC IN SIGHT. I KEPT TFC IN SIGHT AND AT APPROX 2 MI THE JET WAS DSNDING BELOW OUR ALT AND I TOLD MY FO TFC WOULD BE NO FACTOR. THEN TO MY FO'S AND MY SURPRISE; THE JET STOPPED ITS DSCNT AND STARTED TO CLB. EVEN THOUGH I COULD TELL THE JET WOULD PASS WELL OFF OUR L SIDE; I TOLD MY FO TO TURN 20 DEGS R JUST TO MAKE SURE. I NEVER LOST SIGHT OF THE JET; HOWEVER; I WAS CONFUSED AT WHY IT WAS CLBING SINCE WE WERE ABOVE ITS POS. JUST PRIOR TO THE JET BECOMING ABEAM OUR POS AND NOW AT OUR ALT; THE CREW MUST HAVE SEEN US BECAUSE THEY MADE A VERY SHARP R TURN. AT NO TIME DID I OR MY FO FEEL WE WERE IN DANGER OF A MIDAIR AND WERE A LITTLE CONFUSED AT ALL THE MANEUVERING THE JET WAS MAKING. AFTER THE JET PASSED OFF OUR L SIDE AT WINDOW LEVEL I DID NOT FEEL IT WAS CLOSE ENOUGH TO WARRANT EVEN AN EXPLANATION TO THE PAX. I ALSO DO NOT THINK ATC DID ANYTHING UNSAFE OR INAPPROPRIATE.