The current paper provides a comprehensive investigation on the functional and thermodynamical limitations of a hybrid Renewable Energy Sources (RES) - Hydrogen (H2) system. The main principle of this hybrid energy system is the combined utilization of different renewable energy sources in order to cover directly the various loads of an office-type building, while converting excessive energy production to H2 chemical energy via water electrolysis. Finally, the produced gaseous H2, which is compressed in storage tanks, is bound to be used at times of energy shortage to supply either a fuel cell or a H2 burner to produce electrical or thermal power respectively. The prototype system is installed in an office building, located in the Attica region of Lavrion, appropriately renovated in order to host the hydrogen energy production and storage system. The system comprises two RES modules (photovoltaic panels and wind turbines), an alkaline water electrolyzer, a H2 storage system (compressor, gas tanks), a PEM fuel cell and a H2-burner. The building is equipped with various load types whose magnitudes and consumption patterns simulate those of a real office building. The operation of the whole site is conducted through an advanced Energy Management and Control System (EMCS). The outcome of this study reveals the limitations of the system, analyses the energy flow profile of building-RES integration and finally it highlights essential factors that need to be considered for future designing and implementation of RES-H2 systems.