DFW TCASII RA FIRST GIVES DSCNT THEN QUICKLY CHANGES TO CLB RESOLUTION ON DSCNT INTO DFW.

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DFW ARR AT 17000 FT. ATC FACILITY: ZFW. LOCATION: ABOUT 25 MI E OF HOWDY INTXN. ON DSCNT THROUGH 17000 FT ON CEDAR CREEK 4 ARR TO DFW ON CEDAR CREEK ARR; WE GOT A TA OF A LEARJET THAT HAD A VISUAL ON US AND HE WOULD MAINTAIN SEPARATION. WE CALLED LOOKING. I SAW AN ACFT AT 9 O'CLOCK. IT WAS NIGHT. TCASII GAVE US A DSND RA AND THEN ALMOST A SECOND LATER A CLB RA. WE SHOWED THE TFC 200 FT BELOW. IN THE CLB I PICKED HIM UP VISUALLY ON R; 5 O'CLOCK. I ALSO SAW ANOTHER ACFT TO OUR L. THIS INCIDENT WAS ALMOST A VERY BIG MESS. I SUGGEST THE FAA NOT ALLOW NIGHT VISUAL SEPARATION. I BELIEVE THE LEAR WAS LOOKING AT ANOTHER ACFT AND NEVER SAW US OR HE IS A COWBOY GETTING WAY TOO CLOSE TO A COMMERCIAL JET. I BELIEVE THE TCASII CAME VERY CLOSE TO CAUSING A DISASTER WHEN IT GAVE THE DSCNT PRIOR TO THE CLB. IF WE HAD REACTED SLIGHTLY FASTER; THERE WOULD HAVE BEEN A MIDAIR. ANOTHER PLT IN COACH DESCRIBED TO US HOW CLOSE IT WAS. HE SAID THE ACFT DID NOT MOVE IN THE WINDOW UNTIL JUST BEFORE IT CLRED BELOW THE TAIL.