Unitised Regenerative Fuel Cells (URFCs) based on Proton Exchange Membrane (PEM) technology provide a promising opportunity for reducing the cost of the hydrogen subsystem used in renewable-energy hydrogen systems for remote area power supply. A general theoretical relationship between cell potential and current density of a single-cell URFC operating in both fuel-cell and electrolyser modes is derived using the Butler-Volmer equation for both oxygen- and hydrogen- sides, and accounting for membrane resistance and mass transport losses. Modifying the standard Butler-Volmer equation with a denominator term containing two additional 'saturation' parameters to reflect mass transport constraints generates voltage-current curves that are much closer to experimentally-obtained polarisation curves in both modes. The theoretical relationship is used to construct a computer model based on Excel and Visual Basic to generate voltage-current curves in both electrolyser and fuel cell modes for URFCs with a range of membrane electrode assembly characteristics. Hence the influence of key factors such as exchange current densities and charge transfer coefficients on cell performance is analysed. Experimental results for voltage-current curves from singe-cell URFCs with a number of different oxygen-side catalysts are reported, and compared to the theoretically-modelled curves A good match between the theoretical and experimental V-I curves is demonstrated.