A B767 FLC OVERSHOT DEP INTERMEDIATE ALT DUE TO AN FMC AUTOMATION PROB. APCH CTLR GAVE A CLB TO HIGHER ALT BEFORE THE CREW COULD RETURN TO THE OVERSHOT ALT.

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DEPARTING LONDON/GATWICK RWY 8R AND SID SAMZP; WE SELECTED LNAV AT +/-400 FT AGL AND VNAV AT +/-1500 FT AGL. THE FMC WAS PROPERLY PROGRAMMED AND ALL ALTS VERIFIED WITH CHART. THE MCP ALT WAS SET AT 4000 FT; THE SID FINAL ALT. DURING INITIAL CLB; AT ABOUT 1900 FT MSL; FMC WENT INTO ALT CAPTURE MODE. BUT IT DID NOT CAPTURE AT 3000 FT EVEN THOUGH IT WAS IN VNAV AND 3000 FT WAS DISPLAYED. BEFORE COMPLETING THE SID TURN; WE WERE GIVEN A HDG AND CLB CLRNC TO 5000 FT. THERE WERE NO APPARENT CONFLICTS AND ATC MADE NO COMMENT TO US. UPON REVIEW OF HOW THE FMC WAS PROGRAMMED AND HOW WE FLEW THE DEP; WE COULD NOT IDENT THE CAUSE OF THE FMC'S FAILURE TO CAPTURE THE CORRECT ALT. LATER; DURING CLB/LEVELOFF; THE FMC TWICE GAVE US 'CHK TARGET ALT' PROMPTS. UPON INVESTIGATION WE COULD FIND NO REASON FOR THE PROMPTS. THE CONCLUSION THE 3 OF US CAME TO WAS THAT FOR SOME UNRECOGNIZED REASON THE FMC DID NOT CAPTURE THE ALT IT WAS SUPPOSED TO. LATER IN THE FLT DSNDING IN VNAV; THE FMC MADE A VERY 'SLOPPY' ALT CAPTURE. IT MISSED THE PROGRAMMED ALT (FL200) BY ABOUT 100 FT; AND THEN STARTED TO PORPOISE SLIGHTLY APPEARING TO SEARCH FOR THE SET ALT. THIS CAUSED ME TO INTERVENE BY SELECTING ALT HOLD; WHICH STOPPED THE PORPOISING. AGAIN; WE WERE LED TO CONCLUDE THE CAUSE AS AN FMC ANOMALY. UPON ARR AT PHL; WE MADE A LOGBOOK ENTRY.