The present investigation addresses the problem of evaluating the endurance of hybrid electric aircraft and discusses the effect of battery specifications and the engine working points on fuel economy. In particular, the endurance per unit mass of fuel of a hybrid power system is calculated by assuming a constant power-level flight performed with alternate cycles of battery charging and discharging (ON-OFF strategy). The computation of the fuel economy requires accurate models for the time, the power and the energy associated with battery charging and discharge processes. In order to reach this goal, two approaches proposed in literature to evaluate electric endurance were discussed, amended and validated through comparison with experimental data. A model for constant-current/constant voltage battery charge was also presented and validated with literature experimental data. In order to explain how these models can be applied to real applications, a parallel hybrid power system was sized and analyzed for a medium-altitude long-endurance unmanned aerial vehicle. Lithium polymer batteries and two stroke diesel engines were considered and three different hybridization degrees were analyzed. The results showed a trade-off between electric flight time and overall endurance per unit mass of fuel and an improvement up to 12% in fuel consumption with respect to a non-hybrid case with the same engine.