When a steady electric current is passed through a porous membrane which separates two electrolyte solutions at different concentrations the system can, in a suitable experimental configuration and when the current exceeds a critical value, enter a state of stable oscillations of the trans-membrane pressure and potential. In this system, sometimes called the Teorell membrane oscillator, the pressure driven and electro-osmotic flows are opposed. The former is almost independent of the concentration of the solution in the membrane pores; the latter is greater with dilute solutions than with concentrated ones. Oscillatory states can arise when pressure is applied to the concentrated side. Such states have been studied here by using, as membranes, Nuclepore filters which have readily characterized uniform, circular and parallel pores. Several pore sizes, concentrations and electrolytes have been examined. A theoretical treatment of the phenomenon has been developed by assuming that the relaxation rates of the concentration profiles in the membrane pores are large compared with the rates of change of the membrane boundary states during the oscillations. This assumption has permitted the stationary state theory (Meares & Page 1972) to be applied here also. Inertial forces are included but shown to be of little consequence at most times in the apparatus used here. Oscillations are a consequence of the nonlinear character of the equation relating fluid flow in the membrane to the imposed forces. A relatively satisfactory agreement between theory and experiment is found for pressure and potential limit cycles and for flow rates and periodic times. Imperfect mixing in the solution phases is an important complication. It is treated in the theory by the consideration of stagnant membrane boundary films. It appears that at the cycle limits, when the volume flow reverses, the rate of relaxation of these stagnant films may not be large compared with the rates of other processes. This distorts the voltage against time plots from their steady state forms and affects the oscillation times. Inertial and relaxation effects in the membrane at the cycle limits are masked by these effects in the stagnant films. It is suggested that the upper pressure limit may be depressed in practice by the influence of a few large pores which trigger a premature switch from electro-osmotic to hydrostatic pressure control.