This study aims to provide insights into the electrochemical transport and interfacial phenomena in hybrid pseudocapacitors under galvanostatic cycling. Pseudocapacitors are promising electrical energy storage devices for applications requiring large power density. They also involve complex, coupled, and multiscale physical phenomena that are difficult to probe experimentally. The present study performed detailed numerical simulations for a hybrid pseudocapacitor with planar electrodes and binary, asymmetric electrolyte under various cycling conditions, based on a first-principles continuum model accounting simultaneously for charge storage by electric double layer (EDL) formation and by faradaic reactions with intercalation. Two asymptotic regimes were identified corresponding to (i) dominant faradaic charge storage at low current and low frequency or (ii) dominant EDL charge storage at high current and high frequency. Analytical expressions for the intercalated ion concentration and surface overpotential were derived for both asymptotic regimes. Features of typical experimentally measured cell potential were physically interpreted. These insights could guide the optimization of hybrid pseudocapacitors.