A DSNDING C414 HAS AN ENCOUNTER WITH AN ACR ACFT WHILE DSNDING VFR INTO MKE; WI.

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WE DEPARTED VFR FROM CHICAGO MEIGS (CGX) TO WAUKESHA (UES). AFTER DEP CONTACTED CHICAGO APCH FOR VFR ADVISORIES AND CLBED TO 6500 FT. CHICAGO APCH DISCONTINUED ADVISORIES AT THE END OF THEIR AIRSPACE AND SUGGESTED WE CONTACT MILWAUKEE APCH ON 119.65. WE CALLED MKE APCH ON THE SUGGESTED FREQ AND WERE TOLD TO EXPECT ADVISORIES IN 15 MINS. AT THAT TIME WE WERE CURRENTLY 12 MINS FROM OUR DEST AND CONTINUED WITHOUT RA'S. WE BEGAN OUR DSCNT INTO WAUKESHA. AS WE PAST THROUGH APPROX 4600 FT THE PNF NOTICED AN AIRLINER ABOUT 1 MI OFF AT THE 3 O'CLOCK POS THAT WOULD PASS UNDERNEATH US. WE CONTINUED THE FLT AND LANDED AT WAUKESHA WHERE WE WERE ASKED TO CALL MILWAUKEE APCH. MILWAUKEE INFORMED US THAT THE AIRLINER HAD AN RA ON US AND DSNDED IN RESPONSE TO THE RA. THIS ISSUE COULD HAVE BEEN PREVENTED BY: MILWAUKEE APCH PROVIDING RA'S; RATHER THAN DELAYING THEM. BETTER VIGILANCE BY BOTH PLTS IN BOTH ACFT TO SEE AND AVOID. VECTORS BY MKE APCH OF THE AIRLINE TO AVOID OUR PATH ONCE WE BEGAN THE DSCNT (UNLESS THEY HAD US VISUALLY).