AN ACR MLG RPTS THAT THERE MAY HAVE BEEN AN SMA VFR IN IMC.

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ON RADAR VECTORS TO OAK ARPT AT 7000 FT ON TCASII WE NOTICED TFC 400 FT BELOW OUR ALT APPROX 4 NM DIRECTLY AHEAD OF US. SHORTLY AFTER; APCH NOTIFIED US OF THE VFR TFC AT 6600 FT; 2 NM; 12 O'CLOCK. PNF NOTIFIED APCH THAT WE WERE IN IMC CONDITIONS. NO RESPONSE FROM APCH. TCASII CALLED FOR A 1500 FT CLB WHICH WE RESPONDED TO. AT 7400 FT; TCASII CALLED 'CLR OF CONFLICT.' UPON INITIATING THE CLB; WE VISUALLY SAW A 737 AT 8000 FT; 1 MI IN FRONT OF US. ABOUT THE SAME TIME; AS 'CLR OF CONFLICT.' PNF TOLD APCH WE DEVIATED FROM ALT; AT 7400 FT AND RETURNING TO 7000 FT; DUE TO OUR TCASII ALERT. ANOTHER APCH CTLR THEN ASKED US IF WE ARE IN IMC CONDITIONS; WHICH WE RPTED AFFIRMATIVE. HE ALSO ASKED IF THERE WAS ANY WAY THE VFR ACFT WAS IN VMC CONDITIONS; WHICH WE RPTED NEGATIVE. NO FURTHER INCIDENT WAS NOTED. WHEN WE RECEIVED THE TCASII CLB; THE VFR TFC WAS DISPLAYING 200 FT BELOW OUR ALT. THE 737 WAS ALSO DISPLAYED ON OUR TCASII SCREEN; BUT WITH NO VERBAL COMMANDS. SUPPLEMENTAL INFO FROM ACN 271481: WE HAD AN INTERMITTENT BREAK OUT OF THE CLOUDS AND VISUALLY SIGHTED A BOEING 737 SBOUND AT OUT 10 O'CLOCK POS AT 8000 FT AT 2 MI. NO TCASII RA WAS ISSUED FOR THIS TFC. THE BOTTOMS OF THE CLOUD LAYER WERE RAGGED AT APPROX 5000 FT IN THE VICINITY.