A physico-chemical model, not making assumptions about the relative rates of reaction steps is formulated for galvanostatic electrolysis experiments in either the exhaustive or the constant concentration mode. The mathematical formulation (partial differential equations with initial and, in some cases non-linear, boundary conditions) is solved by means of the orthogonal collocation technique and subsequent integration of the ordinary differential equation system in the time domain. The approach is applied to several electrode reaction mechanisms consisting of one or two charge transfer steps. The principal behavior of the simulation program is demonstrated. Electrode reactions are simulated under galvanostatic conditions and results of simulation experiments for the exhaustive and constant concentration modes of the electrolysis are discussed and compared.