Understanding the dynamic response of a solar fuel processing system utilizing concentrated solar radiation and made of a thermally-integrated photovoltaic (PV) and water electrolyzer (EC) is important for the design, development and implementation of this technology. A detailed dynamic non-linear process model is introduced for the fundamental system components (i.e. PV, EC, pump etc.) in order to investigate the coupled system behaviour and performance synergy notably arising from the thermal integration. The nominal hydrogen production power is 2 kW at a hydrogen system effciency of 16-21 % considering a high performance triple junction III-V PV module and a proton exchange membrane EC. The device operating point relative to the maximum power point of the PV was shown to have a differing influence on the system performance when subject to temperature changes. The non-linear coupled behaviour was characterised in response to step changes in water flowrate and solar irradiance and hysteresis of the current-voltage operating point was demonstrated. Whilst the system responds thermally to changes in operating conditions in the range of 0.5-2 minutes which leads to advantageously short start-up times, a number of control challenges are identified such as the impact of pump failure, electrical PV-EC disconnection, and the potentially damaging accentuated temperature rise at lower water flowrates. Finally, the simulation of co-generation of heat and hydrogen for various operating conditions demonstrates the significant potential for system effciency enhancements and the required development of control strategies for demand matching is discussed.