Electrocatalysis of the oxygen reduction reaction (ORR), oxidation of carbon monoxide, and the methanol oxidation reaction (MOR) are all critical to the performance of direct-methanol fuel cells (DMFC). In this work we analysed the activity and mechanism for these reactions at carbon-supported Ru@Pt core-shell catalysts based on measurements of the potential of zero total charge (PZTC) and cyclic voltammetry. The PZTC measured at Ru@Pt is approximately 140 mV lower than at Pt. An analysis of charging curves and complex-capacitance data shows that the lower PZTC cannot be explained exclusively by a lower potential of zero free charge (PZFC). The lower PZTC at the core-shell catalyst therefore indicates that OH adsorbs more strongly on the Ru@Pt than on Pt. From a scaling relation between the free energies of adsorbed oxygen and OH we infer that the lower PZTC value for Ru@Pt implies a larger potential-determining step for the ORR at this catalyst than at Pt. For oxidation of CO and the MOR the stronger binding of OH to the surface at Ru@Pt than at Pt is expected to increase the activity of the former. These predictions are in agreement with the results of measurements of the catalytic activity of the catalysts, and serve to rationalise the catalytic activity of Ru@Pt with respect to those of Pt for these reactions.