VFR SMA DSNDED INTO ACR TFC LEVELLING 500 FT BELOW.

Narrative

DURING DEP FROM MSP INTL ARPT WE WERE ON A VECTOR; HDG 100 DEGS CLBING TO 10000 FT MSL. AS WE PASSED 9000 FT DEP CTL ADVISED US OF VFR TFC; A CHEROKEE; AT OUR 11 O'CLOCK; APPROX 8 MI AT 10500. DEP CTL THEN ADVISED THE CHEROKEE OF US -- A DC-9 PASSING 9000 FT FOR 10000 FT AT HIS 1 O'CLOCK. AS WE LEVELED AT 10000 FT OUR TCASII SHOWED THE CHEROKEE AT 11 O'CLOCK; 5 MI; AND PLUS 600 FT. TCASII ADVISED US TO MONITOR VERT SPD AND SHOWED A RED ARC FROM '0' FPM TO 2500 FPM CLB ON OUR IVSI. BY NOW WE HAD THE CHEROKEE VISUALLY AND ADVISED DEP CTL THAT WE DID. AS THE CHEROKEE APCHED OUR 12 O'CLOCK; WE NOTICED THAT THE CHEROKEE APPEARED TO BE AT OUR ALT (10000 MSL) AND NOT AT 10500 FT. AT THAT MOMENT; THE CHEROKEE ENTERED THE TCASII WARNING AREA AND THE TCASII GAVE A RA DO DSND. A MOMENT PRIOR TO THE TCASII RA; WE HAD BEGUN OUR OWN EVASIVE MANEUVER BY STARTING A L TURN TO AVOID THE CHEROKEE. OUR EVASIVE ACTION RESULTED IN A SLIGHT HDG DEV TO THE LEFT AND A DSCNT OF APPROX 200 FT. WE NARROWLY MISSED THE CHEROKEE AS HE DSNDED THROUGH OUR ALT. APPROX MISS DISTANCE WAS ONLY 200 FT HORIZLY AND LESS THAN 200 FT VERTLY. I BELIEVE THAT; IF WE HAD NOT MANEUVERED; WE WOULD HAVE HAD A MID-AIR COLLISION. SHORTLY AFTER OUR EVASIVE ACTION; OUR TCASII ADVISED 'CLEAR OF CONFLICT.' WE VISUALLY CONFIRMED THAT AND WE RECOVERED TO 10000 FT MSL AND HDG 100 DEGS. SUPPLEMENTAL INFO FROM ACN 268961: I ASKED MINNEAPOLIS APCH: 'THIS IS CALL SIGN; DOES MY TFC HAVE ME?' I RECEIVED NO RESPONSE. I CALLED AGAIN 'CALL SIGN; DOES MY TFC HAVE ME?' AND AGAIN I RECEIVED NO RESPONSE. AT THIS POINT THE AIRLINER LOOKED LIKE IT WAS AT MY ALT DIRECTLY AT 3 O'CLOCK SEVERAL MI AWAY ON A COLLISION COURSE WITH ME AND I HAD NO INDICATION THAT ATC OR THE FLC OF THE AIRLINER HAD ANY INDICATION OF THE SIT. I THEREFORE IMMEDIATELY DSNDED TO TRY TO AVOID THE AIRLINER. THE AIRLINER PASSED BEHIND ME BY PERHAPS 1000 FT AT APPROX THE SAME ALT. AFTERWARD; ATC SAID THAT IN THE ORIGINAL SIT HE HAD PROVIDED 500 FT OF VERT SEPARATION BTWN THE AIRLINER AND ME.