CL60 DEP FROM ORF AT APPROX 4200 FT EXPERIENCED TCAS RA WITH B757 BELIEVED TO BE FROM A MIL ARPT; RECORDS INDICATE AN OPERROR OCCURRED.

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WE DEPARTED ORF ON RWY 5 WITH INITIAL CLB ALT OF 4000 FT. UPON CHKING ON WITH ORF DEP WE WERE GIVEN CLB TO 10000 FT AND L TURN HDG 360 DEGS. AT APPROX 3800 FT WE WERE GIVEN L TURN HDG 250 DEGS. AT APPROX 4200 FT WE RECEIVED A TCAS RA WITH CLB INSTRUCTIONS. THE OTHER AIRPLANE; A B757; ALSO RECEIVED A TCAS RA AND TOLD NORFOLK THEY WERE DSNDING TO COMPLY WITH THE RA. ORF ASKED IF B757 HAD US VISUALLY TO WHICH THEY REPLIED AFFIRMATIVE. WE MAINTAINED OUR 30 DEG BANK IN THE TURN AND CONTINUED THE CLB UNTIL WE RECEIVED THE CLR OF CONFLICT CALL FROM THE TCAS. WE HAD A VISUAL ON THE B757 AND WERE TURNING BEHIND THEM AT THE TIME OF THE TCAS RA. I BELIEVE THE CTLR THOUGHT THAT OUR CLB RATE WOULD PROVIDE ADEQUATE SEPARATION FROM THE B757 WHICH I THINK WAS CLBING OUT OF NAS NORFOLK. IF WE HAD NOT BEEN TURNING; THE CONFLICT WOULD HAVE BEEN CONSIDERABLY CLOSER. I BELIEVE THE CTLR MISSED THE CONFLICT WHEN HE CLRED THE B757 TO CONTINUE THE CLB. THERE WERE NO DEVS FROM ATC DIRECTIONS ON OUR PART; AND NONE THAT WE HEARD FROM THE B757 EXCEPT THEIR RPT OF COMPLYING WITH THE TCAS RA.