An extended theoretical treatment of a two-step surface redox reaction under the conditions of square-wave voltammetry (SWV) is presented. The theoretical model is applicable to any reversibility of both redox steps of the EE reaction. The integral equations representing this theoretical model were solved numerically. The apparent reversibility of the redox steps depends on two dimensionless kinetic parameters, kappa(1) and kappa(2), defined as kappa(1) = k(s,1)/f and kappa(2) = k(s,2)/f, where k(s,1) and k(s,2) are the standard rate constants of the first and second redox steps, respectively, and f is the excitation signal frequency. The response consists of either a single or two separate SW peaks, depending mainly on the difference between the formal potentials of the first and second redox steps as well as on the ratio of the kinetic parameters kappa(1)/kappa(2). The effect of the electron transfer coefficients of both redox steps is also discussed. A part of the theoretical results are qualitatively illustrated by SW voltamograms of the azo-dye Sudan-III.