A DC9 FLC RECEIVED A TCASII RA ON DEP FROM GRB.

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ACFT X DEPARTED GRB RWY 18 ENRTE TO DTW. INITIAL CLRNC WAS 'RWY HDG; MAINTAIN 4000 FT.' UPON CHK IN WITH APCH/DEP CTL; WAS CLRED TO CLB TO 10000 FT AND TURN DIRECT TO FAH VOR (FALLS VOR); HDG WAS APPROX 165 DEGS. AFTER THIS CLRNC WAS RECEIVED; ANOTHER ACFT (ACFT Y) TURBO BEECH 18 CHKED IN WITH APCH; COMING FROM THE S FOR A PRACTICE APCH AND LNDG. ACFT Y WAS AT 8000 FT. GRB DEP DIRECTED US TO FLY A HDG OF 110 DEGS FOR THE CLB. WHILE TURNING TO 110 DEGS; ACFT Y RPTED VISUAL CONTACT WITH OUR ACFT. GRB CLRED THEM TO MAINTAIN VISUAL CONTACT WITH US AND CLRED FOR VISUAL APCH TO GRB. I SIGHTED THE BE18T AT THIS TIME AT MY 2 O'CLOCK POS ON APPARENT COLLISION COURSE. TURNED ON ALL LIGHTS AND XMITTED ON RADIO TO ACFT Y NOT TO DSND. ALSO; RECEIVED RA COMMANDING DSCNT IN EXCESS OF 2000 FPM. FO STARTED DSCNT AND DSNDED APPROX 1000 FT UNTIL CONFLICT PAST. VECTORS FROM GRB APCH PLACED THESE 2 ACFT IN CONFLICT. ALSO; HAD THIS OCCURRED IN DAYLIGHT; PROBABLY WOULD NOT HAVE SEEN OTHER ACFT AS SOON AS WE DID.