NMAC BTWN A MST ACR ACFT AND A MIL FGT ACFT ON A RTE AIRWAY IN THE VIRGIN ISLAND AREA.

Narrative

I WAS DOING MY LAST FLT OF MY SEQUENCE (ACR NUMBER) FROM SAN JUAN; PR; TO SAINT CROIX; VI. ESTABLISHED ON RTE 4 (BY APPROX 1/2 WAY BTWN TUNA INTXN THE COY VOR). WE STARTED OUR INITIAL DSCNT FROM 7000 FT MSL. WE CALLED LEAVING THAT ALT AND BY APPROX PASSING 6300 FT MSL A TFC CAME UP ON THE TCASII SHOWING 300 FT BELOW US AND CLBING. I START LOOKING FOR THE TFC AND IMMEDIATELY AFTER; THE TCASII STARTED ITS RA'S AS FOLLOWS: 'CLB; CLB; CLB;' 'XING ALT;' 'DSCNT; DSCNT; DSCNT.' AT THAT POINT; WE START MANEUVERING THE ACFT (FULL OF PAX) TO COMPLY WITH THE TCASII ADVISORIES; WHILE LOOKING FOR THAT TFC; BUT NO VISUAL CONTACT WAS MADE WITH IT UNTIL THE LAST MIN WHEN SAW IT ON THE R SIDE OF THE ACFT AND FLYING AWAY FROM US. FINALLY; THE ATC TOLD ME THAT THE TFC SUDDENLY CAME UP ON HIS SCREEN AND LATER THEY FOUND OUT IT WAS A MIL FGT ACFT. THIS TFC WAS NOT IN RADIO OR RADAR CONTACT WITH THE SAN JUAN CERAP (ATC). BASED ON THE ADVISORIES RECEIVED FROM THE TCASII THAT TFC WAS MANEUVERING AROUND MY AIRPLANE WHICH I CONSIDERED VERY UNSAFE.