MLG GOT TCASII ON UNKNOWN ACFT AND STARTED A CLB AND TURN PRIOR TO ATC ACTION. ACFT PASSED IN CLOSE PROX ACCORDING TO THE TCASII.

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CRUISING IN CLOUD AT 12000 FT WITH DTW APCH CTL VECTORING TO DTW. RECEIVED TCASII 'TFC' WARNING FOLLOWED BY 'CLB' WARNING. PF IMMEDIATELY BEGAN CLB; AND I ADVISED ATC. CTLR RESPONDED WITH ALT '13000' AND 'L TURN TO 360 DEGS.' TFC PASSED FROM 5 NM AT 10 O'CLOCK ON INITIAL WARNING; 900 FT BELOW CLBING AT 500+ FPM TO 3 O'CLOCK; 400 FT BELOW; AND 2 NM WHILE WE WERE IN OUR L TURN. WARNING CEASED FROM TCASII AFTER TFC PASSED 4 O'CLOCK. WE WOULD HAVE EXPECTED TO RECEIVE TFC INFO FROM OUR CTLR ON POSSIBLE CONFLICTING TFC; ESPECIALLY TFC WITH ALT SQUAWKING TRANSPONDER. WE ARE GUESSING THAT A TURBOJET DEP OUT OF DTW MAY HAVE CAUSED THE CONFLICT. AT ANY RATE; TCASII SAVED US; I BELIEVE. WE NEVER GOT VISUAL CONTACT. ON A LATER FLT; SAME DAY; SAME ACFT; 900 NM SW OF DTW; WE GOT ANOTHER VERY BRIEF 'TFC' AND THEN 'CLB' WARNING FROM OUR TCASII ON A CONFLICTING ACFT WHICH WE DID SEE THROUGH BROKEN CLOUDS AND THE INFO PRESENTED BY TCASII WAS CONFIRMED. TCASII TFC AND RA'S APPEARED RELIABLE WHERE THEY COULD BE CONFIRMED THROUGHOUT THE DAY. SUPPLEMENTAL INFO FROM ACN 196729: INITIAL TCASII TARGET WAS APPROX 6 MI AT 12 O'CLOCK POS; OPPOSITE DIRECTION AND CLBING THROUGH ALT 900 FT BELOW US. AT APPROX 2.5 NM TCASII TARGET PASSED OFF THE R SIDE OF OUR ACFT APPROX 400 FT BELOW US AS WE WERE IN A L TURN FOR AVOIDANCE WHILE IMC. VISUAL CONTACT WITH TARGET WAS NEVER MADE. RECOMMENDATION: ATC CTLR TO ADVISE US OF TFC PRIOR TO TCASII INTERROGATION AND ADVISORIES.