A B757-200 ON APCH AT 3000 FT EXPERIENCED FAILURE OF THE R FMC. FOUND AUTOPLT WOULD NOT DISCONNECT AND CONTINUED INPUTS TO CTLS.

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APCHING ZZZ FROM THE S; SETTING UP FOR APCH AND LNDG TO RWY 8R. EXPERIENCED R FMC FAILURE WHILE COUPLED TO R AUTOPLT. RECEIVED AUTOPLT DISCONNECT AND AUTOTHROTTLE DISENGAGE WARNINGS AND ALERT SOUNDS. HOWEVER; NOTED UNABLE TO GET A CLEAN DISCONNECT FROM R AUTOPLT COUPLE. FO ON ALTERNATE FMC MARRIED DATA RANGES FOR FO HSI COURSE INFO OFF L FMC. USED RAW DATA FOR RWY 8R ILS DME. PROCS GOOD. HOWEVER; AUTOPLT ANOMALY COMPLICATED EVENT. UNABLE TO CLEANLY DISCONNECT R AUTOPLT. USED GANG BAR TO EFFECT COMPLETE AUTOPLT DISCONNECT. AFTER RESEATING AUTOPLT DISCONNECT GANG BAR; UNABLE TO COUPLE UP TO ANY AUTOPLT INCLUDING L AUTOPLT. NOTIFIED APCH CTL OF LOSS OF R FMC. APCH NOTIFIED HEADS UP; PAY MORE ATTN TO OUR FLT. APCH CLRED US TO TURN IN TO INTERCEPT COURSE INTO RWY 8R AND DSND TO 1500 FT MSL. WE EXPERIENCED MORE AUTOPLT DISCONNECT PROBS. NOTIFIED APCH OF DESIRE NOT TO TURN TO INTERCEPT COURSE BUT TO EXTEND FINAL TO WORK WITH ACFT TO CLEAN UP AUTOPLT MALFUNCTION TO CLEAN UP WARNINGS/CAUTIONS AND MAKE SURE AUTOPLTS WERE CLEANLY UNCOUPLED FROM ACFT FLT OP. WE HAD BEGUN OUR DSCNT WHEN APCH STATED; NOT KNOWING WE WOULD HAVE MORE INFLT PROBS; 'YOU DON'T HAVE TO CLB BACK TO 3000 FT; BUT TRY TO LEVEL OFF FOR ME NOW AT 2500 FT UNTIL YOU CAN ACCEPT YOUR COURSE INTERCEPT RWY 8R CLRNC.' WE ACKNOWLEDGED. ACFT WITH AUTOPLTS DISENGAGED PITCHED UP AS FO WAS FLYING. FO APPLIED FORWARD PRESSURE ON CTL TO STOP CLB AT ABOUT 2670 FT MSL. I UTILIZED THE AUTOPLT DISENGAGE GANG BAR ONCE AGAIN AND ACFT FOR FIRST TIME DURING THIS ENTIRE SEQUENCE OF EVENTS FELT FREE OF ANY AUTOPLT INPUT. ADDITIONALLY; DURING THIS EVENT; THE AUTOPLT DISENGAGE BUTTONS ON BOTH CTL COLUMNS APPEARED INOP. NEITHER BUTTON DISENGAGED OR EFFECTED NORMAL CESSATION OF ALERTS. ACFT FLT OP WITH SYS FAILURES AS NOTED HANDLED NORMALLY FROM THIS POINT ON THROUGHOUT LNDG AND TAXI CLR OF RWY. AT THE GATE; ENTERED ALL PERTINENT DATA REGARDING R FMC FAILURE AND AUTOPLT ANOMALY IN LOGBOOK. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THE YOKE SWITCHES; PADDLES AND GANG BAR ALL FAILED TO DISCONNECT THE R AUTOPLT. THE RPTR SAID THE FO HAD TO FIGHT THE CTL INPUTS FROM THE FAILED AUTOPLT UNTIL A DISCONNECT WAS OBTAINED BY HOLDING THE GANG BAR FOR A SLIGHT INTERVAL. THE RPTR STATED THE COMPANY MAINT WILL OFFER NO INFO ON THE CAUSE OF THIS INCIDENT.