B767-300 and 300 ER
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Aircraft Equipment Problem Critical; Deviation / Discrepancy - Procedural Published Material / Policy
Flight Crew Inflight Shutdown; Flight Crew Landed in Emergency Condition; General Flight Cancelled / Delayed; General Maintenance Action
Aircraft
At FL370 noticed an Right 'EEC ALTN' lite. Followed QRH on descent. After following QRH Right engine N1 and EGT began fluxing. Fuel flow slightly higher. As I pushed throttle up fuel flow and N1 continued higher readings than Left Engine. Greater thrust out of left engine evident. With no further relief in QRH and at 13;000 feet getting low on gas and unable to control Right engine ( fuel flow at approximately 11.2 w throttle at idle ) Left engine at idle.  Unable to descend due to high thrust out of Right engine we requested priority handling and shut engine down. Vectored in IMC to ILS Runway XX.
B767-300 Captain found the engine to be uncontrollable so he elected to shut down the Number 2 engine; and made a precautionary landing.