An expression is obtained for the alternating stripping current from a continuous mercury film electrode for a linear potential perturbation. Since the ac depends on the mean surface concentrations of the reduced and oxidized states, it is necessary to solve the dc problem for a linear potential sweep. This is done in two ways : (i) by assuming that the linear sweep can be considered as a series of potential steps and applying the equations developed by Osteryoung and Christie; (ii) by applying the rigorous solution proposed by Garcia. The mean surface concentrations were calculated as a function of the electrode thickness l and the applied potential E. The ac response is analyzed as a function of l, E, and the frequency OMEGA. The results indicate that, at very low l, the ac is a linear function of l and OMEGA. The peak potential shifts in the negative direction as l decreases. For quasi-reversible processes there is a frequency OMEGA(lim) for which the ac is controlled only by charge transfer; OMEGA(lim) increases as the thickness decreases.