B737-300 CREW AND ANOTHER COMPANY ACFT BOTH EXECUTED EGPWS ESCAPE MANEUVERS WITH AN EMER MAX RATE CLB UNTIL THE WARNING STOPPED. BOTH ACFT WERE AT MINIMUM VECTORING ALT AT THE TIME OF OCCURRENCE.

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TERRAIN WARNING. THIS RPT IS BEING SUBMITTED TO IDENTIFY A 'GENERAL OR SPECIFIC' FLT SAFETY CONCERN. THE AIRCREW FOLLOWED/FLEW ESTABLISHED PROCEDURES. OUR FLT WAS ORIGINALLY ASSIGNED THE COMMO ARRIVAL. AT VOLTA WE WERE INSTRUCTED TO PROCEED DIRECT LOCKE. APCHING LOCKE ANOTHER VECTOR WAS ASSIGNED FOR DOWNWIND TO THE ILS RWY 11. WX-IMC/RAIN/LIGHT TURBULENCE. ACFT WAS ESTABLISHED ON AN ASSIGNED ALTITUDE OF 5000 FT. AN EGPWS WARNING FOR TERRAIN WAS RECEIVED; 'TERRAIN-TERRAIN' (ONLY ONE CYCLE OF WARNING). PROCEDURES IMMEDIATELY FOLLOWED; 15-20 DEG NOSE HIGH CLB INITIATED. MSA FOR OUR AREA NOTED AT 5100 FT; AND LEVEL OFF COMPLETED AT 6000 FT. APCH CTL WAS NOTIFIED OF THE WARNING/CLB AT APPROX 5500 FT. APCH WAS CONTINUED TO AN UNEVENTFUL LNDG. TIME OF OCCURRENCE XA55Z-LOCATION-OVER MT. DIABLO (BOTH TIME AND EXACT LOCATION PROVIDED BY BAY APCH CTL). I SPOKE TO THE BAY APCH CTL OPS MGR/SUPVR AFTER LNDG. HE COULD OFFER NO EXPLANATION FOR THE WARNING; BUT DID GIVE ME THE TIME/LOCATION; STATED THERE HAD BEEN NO TFC CONFLICT AS A RESULT OF OUR CLB AND THAT ANOTHER COMPANY FLT; IMMEDIATELY FOLLOWING OUR ACFT; HAD ALSO RECEIVED A TERRAIN WARNING IN THE SAME LOCATION. HE ALSO NOTED THAT BAY APCH WOULD NOT SUBMIT ANY 'TFC CONFLICT RPT' OR OTHER DEVIATION RPT; ONLY THAT THE OCCURRENCE HAD BEEN ENTERED IN HIS ACTIVITY LOG FOR THE PURPOSE OF IDENTIFYING WHAT PROBLEM MAY EXIST. I SPOKE TO THE COMPANY SAFETY REP IN THE A.M. OF 02/FEB/02 ABOUT THE ABOVE OCCURRENCE; AND THAT TWO OF OUR ACFT HAD EXPERIENCED THE SAME OCCURRENCE. HE ADVISED ME TO SUBMIT AN IRREGULARITY RPT AND A SAFETY RPT. SUPPLEMENTAL INFO FROM ACN 537533: THIS RPT IS BEING SUBMITTED TO IDENTIFY A FLT SAFETY CONCERN. OUR FLT WAS ORIGINALLY ASSIGNED COMMO ARRIVAL. AT VOLTA WE WERE INSTRUCTED TO PROCEED DIRECT LOCKE. 5 MIN AFTER WE WERE GIVEN VECTORS AND DSCNTS FOR ILS RWY 11 OAK. WE WERE IMC AT LEVEL 5000 WHEN WE GOT A 'TERRAIN WARNING'. WE BEGAN A CLB AND LET ATC KNOW WE WERE CLBING FOR A TERRAIN WARNING AND WE WOULD LEVEL AT 6000 FT. WE CONTINUED THE FLT TO AN UNEVENTFUL LNDG. AFTER LNDG THE CAPT SPOKE TO BAY APCH. HE COULD OFFER NO EXPLANATION FOR THE WARNING. HE GAVE US THE TIME AND LOCATION AND STATED THERE HAD BEEN NO TFC CONFLICT AS A RESULT OF OUR CLB. HE ALSO SAID THE BAY APCH WOULD NOT SUBMIT ANY 'TFC CONFLICT RPT' OR OTHER DEVIATION RPT.