ACR X TCASII RA. HAD NMAC WITH CPR ACFT Y. VISUAL SEPARATION IN USE; SEE AND AVOID CONCEPT.

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ACR X ON DOWNWIND RWY 35R AT OKC LEVEL AT 6000 FT MSL; ATC ISSUED A CLB CLRNC TO A DEPARTING CPR ACFT Y TO CLB THROUGH OUR ALT BASED ON ACFT Y MAINTAINING VISUAL SEPARATION WITH US. ACFT Y SAID HE HAD US IN SIGHT AND WOULD COMPLY. ATC THEN ADVISED US OF THE CLRNC FOR THE AIRPLANE. AS I WAS LEANING TO LOOK DOWN FOR THE TFC; A RA FIRST TO 'MONITOR VERT SPD' IMMEDIATELY FOLLOWED BY A 'CLB; CLB' AND IMMEDIATELY BY A 'DSND; DSND' OCCURRED. THE FO WAS FLYING AND WAS UNDERSTANDABLY UNCERTAIN WHAT TO DO. I LOOKED OUT AND SAW A FALCON 50 CPR Y (I COULD READ THE NUMBER) IN A STEEP CLB COMING FROM R TO L ON A COLLISION COURSE. THE TIME INVOLVED UP TO THIS POINT APPROX 30 SECONDS TOTAL AND 6 SECONDS FROM THE INITIAL RA. I TOOK EVASIVE ACTION BY TURNING R AND DSNDING; MISSING THE FALCON'S TAIL BY ABOUT 300 FT HORIZ. WE FLEW THROUGH HIS WAKE ABOUT 3 SECONDS AFTER HE PASSED. ROLL AND PITCH RATES WERE NOT EXCESSIVE BUT WERE DELIBERATE. AS THE MANEUVER BEGAN; I KEYED THE YOKE MIKE AND ADVISED ATC THAT WE WERE TAKING EVASIVE ACTION AND HAD AN RA. I CALLED ATC AT OKC TRACON UPON ARR AT THEIR REQUEST AND WAS INFORMED THAT THEY WOULD BE FILING A RPT. SUPPLEMENTAL INFO FROM ACN 315435: ACR X B737 WAS APPROX 10 MI NE OF THE OKC ARPT; HDG 180 DEGS; ASSIGNED 6000 FT MSL. X WAS BEING VECTORED FOR A VISUAL APCH TO RWY 35R. CPR Y DA20 HAD DEPARTED OKC RWY 35R ASSIGNED HDG 010 DEGS AND 5000 FT MSL. I WAS WORKING BOTH ARRS AND DEPS IN THAT AIRSPACE. I ASSIGNED Y HDG 080 DEGS AND MAINTAIN 5000 FT MSL TO ENSURE SEPARATION BTWN Y AT 5000 FT MSL AND X AT 6000 FT MSL. I NEXT EXCHANGED TFC POS WITH BOTH ACFT. Y ADVISED 'TFC IN SIGHT.' I THEN INSTRUCTED Y TO 'MAINTAIN VISUAL SEPARATION AND CLB AND MAINTAIN 15000 FT.' X NEXT RPTED A TCASII RA TO CLB. THE PLT OF ACFT X NEXT STATED THAT HE WAS DECLARING A 'NEAR MISS AND FILE THE PAPERWORK.' I THEN SWITCHED X TO THE FINAL CTLR FREQ. I ADVISED THE PLT OF ACFT Y OF THE INCIDENT AND THEN SWITCHED THE ACFT TO THE ARTCC FREQ. I DO NOT KNOW IF X ACTUALLY INITIATED A CLB IN CONFORMANCE WITH THE TCASII ADVISORY; BUT IF SO; THIS COULD HAVE CONFUSED Y AS TO WHAT X WAS GOING TO DO. THEREBY MAKING VISUAL SEPARATION MORE DIFFICULT.