Nowadays the use of heat pumps is spread widely in new and refurbished high-efficient buildings. Heat pumps can be very efficient but their energy performance is influenced by the temperature of their external thermal reservoir which can be unstable during the heating season (i.e. outdoor air) and characterized by low values. For this reason, the thermal capacity of the heat pump decreases in the colder days and in order to match the maximum heating load of a building the unit must be slightly oversized. A suitable solution to avoid the energy losses due to an excess of on-off cycles during the milder part of the season is the adoption of a hybrid system, consisting of a heat pump, sized to partially cover the peak load of the building, coupled to a second heat generator (back-up device). The aim of this paper is to assess the influence of the heat pump sizing, the unit cycling losses and the typology of back-up system on the seasonal performance of a heating plant based on a hybrid generator obtained by coupling a single-stage on-off air-to-water heat pump to a back-up device (electrical heater or gas boiler). In this work, the dynamic model of the hybrid heat pump system is presented; several simulations were performed to assess the seasonal energy performance of the system coupled to a single-family house located in Bolzano (Italy) and to compare it with those of monovalent heating systems based on an air-to-water heat pump or a gas boiler only. The analysis enables to evaluate the energy savings achievable by employing a hybrid system in which the generators can work in parallel or alternatively and to study the influence of the cut-off temperature on the seasonal performance of the system. Results point out that hybrid systems can be a suitable solution to achieve significant energy savings with respect to the classical monovalent systems. More in detail, the largest seasonal efficiency was obtained by selecting a heat pump sized to cover the half of the building peak load and by setting a control logic in which back-up and heat pump work in parallel: the introduction of a cut-off temperature larger than the design external temperature is not beneficial. It is demonstrated that an energy savings close to 16% can be achieved by adopting a hybrid system (air-to-water heat pump + gas boiler) if compared to a traditional heating system based on a single gas boiler, even in presence of an undersized heat pump.