ACFT EQUIP PROB. R ENG ELECTRONIC ENG CTL; EEC; AND ENG LIMITER CTL; ELC; LIGHTS CAME ON DURING DSCNT WITH ACCOMPANYING AUTOTHROTTLE DISCONNECT. AIRSPD GOT SLOW WHEN AUTOTHROTTLES DIDN'T ADVANCE AT LEVEL OFF. THRUST LEVERS PUSHED UP MANUALLY WITH RESULTANT COMPRESSOR STALL AND CAUSING ACRID SMOKE TO ENTER ACFT CABIN. EMER DECLARED AFTER A GAR FOR SLOW TFC ON FINAL.

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A DSCNT CLRNC WAS RECEIVED TO FL240 AND SLOW TO 250 KTS. THE DSCNT WAS MADE IN FLT LEVEL CHANGE WITH IDLE THRUST. UPON LEVEL OFF ABNORMAL INDICATIONS WERE OBSERVED. THE R ENG EEC AND ELC LIGHT CAME ON WITH A AUTOTHROTTLE DISCONNECT. THE LEVEL OFF HAD JUST BEEN ACCOMPLISHED SO THE THRUST LEVERS MAY HAVE BEEN AT IDLE OR JUST ADVANCING TO THE MID-POS. OUR INVOLVEMENT WITH THE CHKLIST AND DEPENDENCY ON AUTOTHROTTLES HAD ALLOWED THE AIRSPD TO REDUCE TO APPROX 210 KTS. THE THRUST LEVERS WERE ADVANCED WITH NO ENG RESPONSE. I FURTHER ADVANCED THE PWR TO ESTABLISH OUR ASSIGNED SPD AND OBSERVED VERY SLOW ACCELERATION. NOT SATISFIED WITH THRUST RESPONSE AND SLOW AIRSPD INCREASE I PROMPTLY PUSHED THE THRUST LEVERS FORWARD AND EXPERIENCED A NOTABLE COMPRESSOR STALL FROM THE R ENG. ENG INST INDICATIONS WERE NORMAL. THE PAX CABIN WAS FILLED WITH AN ACRID ODOR AND TRACE OF SMOKE. WE INFORMED ATC OF OUR PROB AND CONTINUED THE ARR TO RWY 25R. AFTER SEVERAL VECTORS WE WERE NOW CLRED FOR THE APCH TO RWY 24R. AT THE FINAL FIX WE WERE INSTRUCTED TO GAR BECAUSE OF SLOW TFC. UPON APPLICATION OF THRUST THE ACRID ODOR WAS AGAIN ENTERING THE CABIN. WE DECLARED AN EMER TO EXPEDITE OUR APCH AND LNDG. I CONSIDER THE DECISION TO DECLARE AN EMER PRUDENT BECAUSE THE STATUS OF THE ACFT AND SYS WAS UNKNOWN; THE WORKLOAD WAS HIGH AND FUEL WAS APCHING 8500 LBS. WE WERE IMMEDIATELY VECTORED BACK AND MADE A NORMAL LNDG. THE FIRE DEPT INSPECTED THE ENG AND WE PROCEEDED TO THE GATE. IN DISCUSSION WITH MAINT ROLLS ROYCE HAS ISSUED AN AIRWORTHINESS DIRECTIVE TERMED 'RUN DOWN.' THIS IS A FUEL CTL PROB THAT RESULTS FROM DSCNT WITH IDLE THRUST RESULTING IN A NEAR FLAMEOUT CONDITION WITH SLOW THRUST RESPONSE. EMPHASIZE LESS DEPENDENCY ON AUTOMATION (AUTOTHROTTLES). GAIN MORE KNOWLEDGE CONCERNING 'RUN DOWN' AND OPERATING PROCS OR CORRECTIVE MAINT TO AVOID THIS ANOMALY.