This paper presents a full and partial load exergy analysis of a hybrid SOFC-GT power plant. The plant basically consists of: an air compressor, a fuel compressor, several heat exchangers, a radial gas turbine, mixers, a catalytic burner, an internal reforming tubular solid oxide fuel cell stack, bypass valves, an electrical generator and an inverter. The model is accurately described. Special attention is paid at the calculation of SOFC overpotentials. Maps are introduced, and properly scaled, in order to evaluate the partial load performance of turbomachineries. The plant is simulated at full-load and part-load operation, showing energy and exergy flows trough all its components and thermodynamic properties at each key-point. At full-load operation a maximum value of 65.4% of electrical efficiency is achieved. Three different part-load strategies are introduced. The off-design operation is achieved handling the following parameters: air mass flow rate, fuel mass flow rate, combustor bypass, gas turbine bypass, avoiding the use of a variable speed control system. Results showed that the most efficient part-load strategy corresponded to a constant value of the fuel to air ratio. On the other hand, a lower value of net electrical power (34% of nominal load) could be achieved reducing fuel flow rate, at constant air flow rate. This strategy produces an electrical efficiency drop that becomes 45%.