NMAC BTWN A CL65 AT NIGHT ON FINAL APCH AT 500 FT AGL TO A NON TWR ARPT AND A CPR JET COMING AT THEM WITH NO LIGHTS ON. THE RPTR IN THE CL65 TOOK EVASIVE ACTION.

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UPON ARR AT GRR; WE ADVISED ATC WE HAD RWY 17 IN SIGHT. WE WERE CLRED FOR THE VISUAL APCH. ZAU RPTED VFR TFC IN THE PATTERN AT GRR AND WE WERE TOLD RADAR SVC TERMINATED; RPT DOWN TIME OR CNX TIME THIS FREQ. UPON JOINING FINAL; I NOTICED WHAT APPEARED TO BE AN ARPT ON FINAL FOR RWY 26R (WE WERE LINED UP ON RWY 17) WE WERE CONVERGING ON THE RWY AND JUST UNDER 500 FT AGL; I ELECTED TO GO AROUND. THE FO WAS THE PF. AFTER THE STANDARD CALLS; I LOOKED DOWN LONG ENOUGH TO RAISE THE FLAPS AND GEAR. WHEN I LOOKED UP; THE JET WAS IN OUR WINDSCREEN; IN A HARD BANKING L TURN. I TOOK THE CTLS AND BANKED HARD L; WE MISSED THE OTHER ACFT BY APPROX 100 FT/VERT 0 FT. THE FO STATED ALL HE SAW WAS THE BELLY OF THE ACFT IN OUR WINDSCREEN. BOTH OF US NOTED WE SAW NO LIGHTS ON THE AIRPLANE; AS WELL AS NOT RECEIVING ANY TCASII WARNINGS. THE ACFT APPEARED TO BE LIGHT GREY. HOWEVER; IT WAS DARK AND HARD TO TELL. WE WERE MONITORING CTAF AS PER COMPANY PROCS AND ANNOUNCING OUR POS. NEITHER OF US HEARD THE OTHER ACFT IN THE PATTERN. I KNOW WE HAD THE CORRECT FREQ AND VOLUME AS IT WAS PLT CTL LIGHTING. AS WELL AS THE RPT FROM ATC THERE WAS VFR TFC. A B727 ON THE GND SAW THE WHOLE THING UNFOLD AND STATED HE WASN'T SURE IF THE GUY WAS MAKING ANNOUNCEMENTS OR NOT; AS HE WAS MONITORING CTR FREQ ON CTAF. OTHER -- THE TWR HAD BEEN CLOSED FOR APPROX 5-10 MINS BEFORE OUR APCH. ZAU DID A GREAT JOB ADVISING US OF TFC TARGETS IN THE AREA. IT IS POSSIBLE THE OTHER ACFT WAS NOT A CITATION.