MD11 FLT CREW HAS A TCAS RA DURING DEP FROM OAK AND MAINTAINS TCAS PRESCRIBED MANEUVERS.

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ON DEP FROM OAKLAND WITH FO FLYING; AND JUST AFTER INITIAL CHK-IN WITH NORCAL CTL; WE RECEIVED A TA; WHICH WAS QUICKLY FOLLOWED BY AN RA (TO MAINTAIN VERT SPD). SINCE RWY 11 WAS IN USE AT OAKLAND AND WE WERE FLYING THE MARINA 4 SID; MY FIRST INSTINCT AFTER THE AURAL TA WAS THAT THE TFC MUST BE IN THE PATTERN AT HAYWARD ARPT. A SCAN OF THE PFD INDICATED TFC IN THAT AREA; BUT THE PROB BOGIE THAT WAS SPOTTED AMBER; THEN QUICKLY TURNED RED; WITH THE ONE TO THE FRONT RIGHT OF OUR ACFT; A HVY JET OFF SAN FRANCISCO. THE RA ANNOUNCED; 'MAINTAIN VERT CLB!' AS THE WX WAS MARGINAL IN MOST QUADRANTS I MADE QUICK NOTE THAT THE FO WAS FOLLOWING THE PROPER INSTRUCTIONS FOR THE RA THEN LOCATED VISUALLY THE TFC OUT THE R SIDE OF OUR ACFT. IT WAS GREATLY DECREASING IN DISTANCE AND SLIGHTLY CHANGING BEARING ALONG WITH A STEADY ALT THAT ALLOWED US TO AVOID EACH OTHER SINCE WE WERE MAINTAINING OUR CLB. THE CREW IN THE OTHER PLANE SEEMED A BIT PERTURBED WITH THE CTLR IN COMS AT THAT POINT AND FOLLOWING; AND STATED AT THEIR FREQ CHANGE THAT THEY WERE GOING TO FILE A RPT. THEIR VECTORING CAUSED THEM TO PASS BEHIND OUR ACFT BUT ON AN EASTERLY COURSE IN THE GENERAL DIRECTION THAT WE WERE ALSO TURNED. WE WERE SWITCHED TO ANOTHER CTLR SHORTLY AFTER; AND IN COM WITH THE CTLR BEFORE LEAVING THE FREQ; I INFORMED THEM THAT WE HAD AN RA IN THE PROCESS OF THE DEP AND PASSING TFC.