A large portion of fuel energy is wasted through the exhaust of internal combustion engines. Turbocompound can, however, recover part of this wasted heat. The energy recovery depends on the turbine efficiency and mass flow as well as the exhaust gas state and properties such as pressure, temperature and specific heat capacity.The main parameter influencing the turbocompound energy recovery is the exhaust gas pressure which leads to higher pumping loss of the engine and consequently lower engine crankshaft power. Each air-fuel equivalence ratio (λ) gives different engine power, exhaust gas temperature and pressure. Decreasing λ toward 1 in a Diesel engine results in higher exhaust gas temperatures of the engine. λ can be varied by changing the intake air pressure or the amount of injected fuel which changes the available energy into the turbine. Thus, there is a compromise between gross engine power, created pumping power, recovered turbocompound power and consumed compressor power.In this study, the effects of different λ values and exhaust back-pressure have been investigated on the efficiency of a heavy-duty Diesel engine equipped with a single-stage electric turbocompounding. A one-dimensional gas dynamics model of a turbocharged engine was utilized that was validated against measurements at different load points. Two configurations of turbocompound engine were made. In one configuration an electric turbocharger was used and the amount of fuel was varied with constant intake air pressure. In another configuration the turbocharger turbine and compressor were disconnected to be able to control the turbine speed and the compressor speed independently; then the compressor pressure ratio was varied with constant engine fuelling and the exhaust back-pressure was optimized for each compressor pressure ratio.At each constant turbine efficiency there is a linear relation between the optimum exhaust back-pressure and ideally expanded cylinder pressure until bottom dead center with closed exhaust valves. There is an optimum λ for the turbocharged engine with regard to the fuel consumption. In the turbocompound engine, this will be moved to a richer λ that gives the best total specific fuel consumption; however, the results of this study indicates that turbocompound engine efficiency is relatively insensitive to the air-fuel ratio.