A model for the prediction of the current-voltage characteristics of a two electrodes cell incorporating the dynamics of the gas film formed during the electrochemical discharge phenomenon is developed. In its mean-field version, the model presents good qualitative agreement but overestimates the hysteresis effect and predicts too large current densities for the cell operation once the gas film is formed. An improved stochastic model, which assumes gas film departures from the electrode surface according to a Poisson process, addresses these issues and gives significantly better predictions. Two relations are presented which allow estimating the mean gas film detachment time and its variance from the experimental study of the hysteresis in the forward and reverse scan of a two electrode cell operated at high current densities.