We consider theoretical models for CO monolayer oxidation on stepped Pt single-crystal electrodes and Ru-modified Pt(111) electrodes. For both systems, our aim is to assess the importance of CO surface diffusion in reproducing the experimental chronoamperometry or voltammetry. By comparing the simulations with the experimental chronoamperometric transients for CO oxidation on a series of stepped Pt surfaces, it was concluded that mixing of CO on the Pt(111) terrace is good, implying rapid diffusion (N. P. Lebedeva, M. T. M. Koper, J. M. Feliu and R. A. van Santen, J. Phys. Chem. B, submitted). We discuss here a more detailed model in which the CO adsorbed on steps is converted into CO adsorbed on terraces as the oxygen-containing species occupy the steps (as observed experimentally on stepped Pt in UHV), followed by a subsequent oxidation of the latter, to reproduce the observed chronoamperometry on stepped surfaces with a higher step density. On Ru-modified Pt(111), the experimentally observed splitting of the CO stripping voltammetry into two stripping peaks, may suggest a slow diffusion of CO on Pt(111). This apparent contradiction with the conclusions of the experiments on stepped surfaces, is resolved by assuming a weaker CO binding to a Pt atom which has Ru neighbors than to bulk Pt(111), in agreement with recent quantum-chemical calculations. This makes the effective diffusion from the uncovered Pt(111) surface to the perimeter of the Ru islands, which are considered to be the active sites in CO oxidation electrocatalysis on PtRu surfaces, very slow. Different models for the reaction are considered, and discussed in terms of their ability to explain experimental observations.