WHILE FLC OF A MD83 WERE DEVIATING AROUND WX UNDER ATC CONCURRENCE WITH NO ASSIGNED HEADING OR TRACK; LESS THAN LEGAL SEPARATION OCCURRED WITH A BEECH; BE60; DUKE.

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I WAS FO ON ACR X FLT NUMBER FROM COS TO LAS. THE CAPT WAS XX. ACFT WAS A MD83 INBOUND TO LAS FROM COS. ZLA CLRED US TO DSND TO 17000 FT DIRECT TO CROWE INTXN. AFTER WE LEVELED AT 17000 FT WE ASKED FOR CLRNC TO DEVIATE R OF COURSE FOR WX. THE REQUEST WAS APPROVED. BOTH PLTS UNDERSTOOD IT TO MEAN THAT AFTER CLR OF WX WE WERE TO COMPLY WITH OUR LAST CLRNC SINCE NO ASSIGNED HEADING WAS GIVEN. (OUR LAST CLRNC TO CROWE.) ONCE CLR OF THE INITIAL WX WE TURNED L TO GO DIRECT TO CROWE AND TO AVOID OTHER WX. DURING THIS TIME WE MAINTAINED OUR ASSIGNED ALT OF 17000 FT. THE AUTOPLT WAS ENGAGED WITH THE FO FLYING. EARLIER THE CTLR HAD ADVISED US OF A DUKE ACFT WHICH WAS AT 16000 FT IMC. THE CTLR NEVER ASSIGNED A HEADING UP TO THIS TIME AS WE PROCEEDED BACK TO CROWE INTXN. WE WERE THEN CLRED TO 11000 FT. AS WE PASSED 14500 FT THE CTLR ASKED IF WE HAD TURNED L WHICH WE ACKNOWLEDGED. THE CTLR THEN ASSIGNED A HDG OF 330 DEGS AND SAID WE MAY HAVE CONFLICTED WITH THE DUKE ACFT. THIS WAS AT APPROX XA43 Z DAYLIGHT HRS WITH A FEW OR MORE WX CELLS IN THE IMMEDIATE AREA. THE ACFT TCASII WARNING SYS NEVER WENT OFF.