FLC OF A WDB CLBED IN RESPONSE TO A TCASII RA DURING A STAR ARR RESULTING IN A CRITICAL AIRBORNE CONFLICT. THE OTHER ACFT WAS INSTRUCTED BY THE ARTCC CTLR TO MAINTAIN VISUAL SEPARATION WITH RPTR'S ACFT DURING THEIR CLB.

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ON THE PULLMAN ARR PASSING FL180; WE RECEIVED A TCASII TA FOLLOWED BY AN RA COMMANDING US TO REDUCE DSCNT RATE. WE COMPLIED WITH RA COMMAND AND LEVELED OFF AT OUR ASSIGNED ALT OF 16000 FT. ATC GAVE US A CLRNC TO DSND TO 10000 FT; BUT WE ALSO GOT A CLB RA. I INITIATED A CLB TO COMPLY WHILE MY FO TOLD ATC THAT WE WERE UNABLE TO COMPLY WITH DSCNT CLRNC. AN ACR Y FLT HDG SE CROSSED OUR FLT PATH CLOSE IN FRONT OF US AT OUR ALT. A FEW SECONDS AFTER THIS; WE RECEIVED A TCASII 'CLR OF CONFLICT.' WE QUESTIONED ATC; AND WERE TOLD THAT THE ACR Y FLT HAD US IN SIGHT AND HAD REQUESTED A VISUAL CLB. ATC HAD GRANTED THE REQUEST TELLING THE ACR Y FLT TO MAINTAIN VISUAL SEPARATION FROM US. THE ACR Y PLT RESPONDED TO US AND ATC THAT HE HAD MISJUDGED HIS RATE OF CLB AND HIS SEPARATION FROM OUR FLT; AND HE APOLOGIZED. THIS WAS TOO CLOSE AND SAFETY WAS COMPROMISED. THE PROB: 1) ATC GIVES VISUAL CLBS OR DSCNTS WITHOUT BOTH ACFT HAVING EACH OTHER IN SIGHT (ONLY 1 REQUIRED). 2) DIFFERENT CARRIERS HAVING DIFFERENT PROCS WHEN THEY RECEIVED TCASII RA. THIS TIME ONE CARRIER MUST FOLLOW RA COMMANDS; THE OTHER CARRIER IS CAPT'S DISCRETION. THESE 2 PROBS MUST BE CORRECTED BEFORE IT IS TOO LATE.