A DEP B767-300 CARGO FLT HAS AN NMAC AT 4500 FT WITH A DEP DC8 CARGO FLT 10 MI SW OF SDF; KY.

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DURING DEP FROM RWY 17R AND PASSING APPROX 4500 FT MSL ON AN ASSIGNED HDG OF 190 DEGS; WE RECEIVED A TCASII TA FOR OUR 12 O'CLOCK POS. I QUICKLY GLANCED OUTSIDE TO SEE AN ACFT BELOW OUR ALT; IN A R TURN AND LESS THAN 1 MI. IMMEDIATELY; I RECEIVED A TCASII RA OF 'DSND; DSND.' CONSIDERING MY POS RELATIVE TO THE TFC AND CLB RATE; I ELECTED TO INCREASE MY CLB RATE; TAKE EVASIVE ACTION; AND AVOID THE TFC VISUALLY. IMMEDIATELY FOLLOWING THIS RA; THE RA 'MONITOR VERT SPD' WAS BROADCAST. MY ACTIONS WERE TO SAFELY CLR THE TFC BY MAINTAINING A HIGH VERT SPD. THE TFC WAS NEVER CALLED OUT BY THE DEP CTLR. I QUERIED THE CTLR WHEN THE TFC WAS FIRST ACQUIRED AND HE RESPONDED WITH 'NEGATIVE' OR 'NO TFC.' AFTER THE TFC PASSED US; THE CTLR THEN RESPONDED WITH 'HE IS 1000 FT BELOW YOU.' I ASKED THAT THE TAPE 'BE MARKED.' A JUMP SEATER; FAMILIAR WITH THE B767; REMARKED THAT THE ACFT PASSED VERTLY BELOW US AT 300 FT AS INDICATED BY TCASII. MY FO ESTIMATED HORIZ DISTANCE AT 300-500 FT. ALTHOUGH THE VISIBILITY WAS EXCELLENT; TCASII WAS MY FIRST INDICATION OF A TFC CONFLICT AND CERTAINLY WAS A LIFE SAVER IN RESOLVING THIS POTENTIALLY DANGEROUS SIT. IN A DISCUSSION WITH THE CREW OF THE OTHER ACFT; THEY DEPARTED FROM RWY 17L AND WERE GIVEN A R TURN DIRECT TO ABBY; ACROSS MY DEP PATH.