AN MD80 FLC HAD AN NMAC DEPARTING SJC.

Narrative

DEPARTED ON THE LOUPE 9 DEP. CLR SKIES WITH VISIBILITY OF 10 MI. IN THE DEP TURN; BAY APCH SAID TO EXPECT TFC AT 9 O'CLOCK WHEN WE LEVELED OUR WINGS. WE WERE JUST LEVELING ON A HDG OF 120 DEGS CLBING THROUGH 4400 FT WHEN THE TCASII SAID 'TFC.' AT 4600 FT WE HAD AN RA SAYING DSND. IMMEDIATELY THEREAFTER THE CTLR SAID 'CLB TO 12000 FT; EXPEDITE YOUR CLB.' THE TCASII SHOWED TFC DIRECTLY AHEAD 500 FT ABOVE US WHEN THE 'TFC' SOUNDED. AT THE RA (DSND) IT SHOWED TFC 200 FT ABOVE IN FRONT. AT THAT TIME I SPOTTED THE TWIN CESSNA AND TURNED THE ACFT TO THE R TO AVOID COLLISION. THE FO; WHO WAS FLYING; THEN SAW THE TFC. WHEN THE CTLR SAID TO CLB TO 12000 FT; HE DID SAY THE TFC HAD US IN VISUAL CONTACT. AT THE TIME OF OUR EVASIVE MANEUVER; IT LOOKED LIKE THE CESSNA JUST SAW US AND VEERED TO THE R. THE PLT RIDING IN OUR JUMP SEAT SAID HE COULD ALMOST SEE THE FACE OF THE CESSNA PLT. THE OTHER ACFT SAID HE HAD US IN VISUAL CONTACT. WE ARE NOT SURE OF THAT. WE WERE ON A SID IN A TURN AND COULDN'T VISUALLY SEE THE TFC UNTIL THE LAST MIN. THIS INCIDENT COULD EASILY HAPPEN AGAIN AND A MIDAIR COLLISION COULD EASILY TAKE PLACE.