A theoretical study of coupled electron-proton transfer is presented for heterogeneous electron transfer to redox centers attached to electrodes. Proton transfer steps are assumed to be at equilibrium and the transfer coefficients are assumed to exhibit the potential dependence predicted by Marcus Density-of-States theory. Five cases are considered: 1e1H, 1e2H, 2e, 2e1H, and 2e2H. Procedures are given for calculating the apparent standard rate constant, the apparent transfer coefficient, and the path of electron transfer as a function of overpotential and pH. The behavior of these parameters are compared with a previous theoretical treatment in which the transfer coefficient for each electron transfer step was assumed to be 0.5 independent of overpotential. The predictions of the two treatments are qualitatively similar but quantitatively different. In particular, when the transfer coefficient depends on the electrode potential, apparent standard rate constants are smaller, asymmetrical Tafel plots appear in the 1e1H and 1e2H cases, and the path of electron transfer depends on potential as well as pH. Experimental evidence for the validity of the model is described.