Abstract. Biological membranes are capacitors that can be charged by applying an electric field across the membrane. The charges on the capacitor exert a force on the membrane that leads to electrostriction, i.e., a thinning of the membrane. This effect is especially strong close to chain melting transitions. A consequence is voltage induced pore formation in the lipid membrane. Since the force is quadratic in voltage, negative and positive voltages have an identical influence on the physics of symmetric membranes. This is not the case for a membrane with an asymmetry leading to a permanent electric polarization. Positive and negative voltages of identical magnitude lead to different physical properties. Such an asymmetry can originate from a lipid composition that is different on the two monolayers of the membrane, or from membrane curvature. The latter effect is called flexoelectricity. It was investigated in detail by A.G. Petrov in the recent decades. As a consequence of permanent polarization, the membrane capacitor is discharged at a voltage different from zero. This leads to interesting electrical phenomena such as outward or inward rectifcation of membrane permeability. The changes in current-voltage relationships are consistent with the known magnitude of the flexoelectric effect.