B737 ON APCH TO OAK EXPERIENCED NEAR MISS WITH VFR XING TFC.

Narrative

WHILE PROCEEDING TO MITOE ON THE ILS RWY 29 AT OAK; WE WERE CLRED TO DSND TO 2000 FT UNTIL 6 DME; CLRED VISUAL APCH TO RWY 29. AS WE PROCEEDED INBOUND; WE DSNDED AND SLOWED TO CONFIGURE. WE LISTENED AS APCH ATTEMPTED TO GET RADIO CONTACT WITH A VFR ACFT HEADING TOWARDS OAK. ABOUT 10 DME FROM OAK ARPT; DSNDING THROUGH 3500 FT; NORCAL APCH CALLED OUT TFC AT OUR 9-10 O'CLOCK POS. AT APPROX 2500 FT; NORCAL TOLD US THE TFC WAS NORDO AND TO STOP DSCNT UNTIL IT WAS IN SIGHT. THE CAPT IMMEDIATELY ACQUIRED THE TFC AT OUR 9-10 O'CLOCK POS AND RPTED IN SIGHT. I HAD LEVELED AT 2300 FT AND BEGAN MY TURN TO FINAL. THE CAPT POINTED OUT THE TFC TO ME; WHICH WAS APCHING US AT CO-ALT. I VISUALLY ACQUIRED THE TFC AND BEGAN A SLIGHT CLB AND TURN AWAY. THE CAPT STATED 'PREPARE FOR A POSSIBLE GAR' AS THE TFC APCHED. I LOOKED OVER AT THE TFC AGAIN AND SAW IT INITIATE A DSCNT. WE WERE NOW ON FINAL OVER HAYWARD ARPT AT ABOUT 6 DME FROM OAK. WE NEXT RECEIVED A TA FOR TFC SHORTLY FOLLOWED BY AN RA TO CLB. THE CAPT MAINTAINED VISUAL WITH THE TFC AS I FOLLOWED THE RA. THE TFC PASSED BEHIND US; WE CONFIGURED AND COMPLETED A NORMAL UNEVENTFUL APCH AND LNDG AT OAK. DURING THE EVENT; NORCAL CONTINUED TO ATTEMPT CONTACT WITH THE TFC. WHILE ON SHORT FINAL ON TWR FREQ 127.12; WE FINALLY HEARD TWR TALKING TO THE ACFT. IT APPEARED TO BE A PIPER MALIBU. AT THE CLOSEST POINT IT PASSED US CO-ALT; APPROX 300 FT LATERAL FT AWAY.