LGT WITH GLASS COCKPIT; AUTOPLT ON HAS ABRUPT NOSE PITCH DOWN WHEN SELECTING VNAV. AUTOPLT TURNED OFF BUT VERY DIFFICULT TO PULL NOSE BACK UP. FO PROGRAMMING FOR APCH AS SCREEN GO BLANK.

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ACFT WAS ON AUTOPLT; RTE WAS PROGRAMMED INTO FMC THROUGH ILS 24R APCH. CROSSED FIM ON PROFILE APPROX 16000 FT. SET 12000 IN ALT AND STARTED SLOWING TO PROFILE SPD 280 KTS. ON REACHING SPD AND ON PROFILE (ABOVE 12000) AT SYMON FO SET 10000 IN ALT FOR BAYST. I RESELECTED VNAV AND THE ACFT RESPONDED WITH A VERY DRAMATIC NOSE DOWN PITCH. I PUNCHED THE AUTOPLT OFF AND STARTED PULLING THE NOSE BACK UP. ALT WAS APPROX 11500; VERT SPD PEGGED ON 6000 DOWN; SPD WITH SPOILERS UP WAS GOING THROUGH 300 KTS. OUTSIDE VIEW LOOKED LIKE A HIGH DIVE. I WAS PULLING A VERY GOOD G LOAD TO REGAIN LEVEL FLT. FULL RECOVERY WAS REACHED ABOUT 9780. NO ALT ALERT SOUNDED IN COCKPIT. I HAND FLEW THE BAL OF THE FLT. AFTER SMO ON ASSIGNED HDG THE FO TRIED TO EXTEND THE OM (ROMEN) FOR INTERCEPT FOR ILS 24R (ARPT WAS 500 OVCST; TOPS ABOUT 1500). WHEN ROMEN WAS TAKEN FROM SCRATCH PAD TO INTERCEPT BOX; THE WHOLE THING WENT BLANK. HE SELECTED ANOTHER FMC AND RE-INSTALLED THE APCH FOR A HAND FLOWN ILS. FLT WAS MET BY R AND E'S THAT VERIFIED THE R FMC HAD FAILED. NO INDICATION OF FAILURE BEFORE GOING BLANK; BUT IT SURE WANTED TO DO SOMETHING (PITCH-WISE) THAT WASN'T PROGRAMMED. YOU CAN GET BUSY REAL FAST WHEN ALL THE MAGIC FAILS THAT CLOSE TO LNDG. I HOPE NEW LOW TIME PEOPLE MOVING ALMOST DIRECTLY INTO GLASS COCKPITS DON'T RELY TOO MUCH ON AUTOMATION AND FORGET HOW TO FLY. MY OPINION -- IT'S GREAT BUT DON'T EVER TRUST IT.