Film capacitors have a thin carrier film (1) as dielectric. The surfaces of the carrier films are provided with conductor layers (2) - serving as electrodes - made of metal or made of a nonmetallic conductor. If the capacitor is charged during operation, electric fields with large field strengths can arise at the edges of the conductor layers (2), which can lead to breakdowns. The invention is essentially distinguished by the fact that an edge zone coating (3) is present at the edges of the electrodeforming conductor layer (2), which edge zone coating is only partly charged in the time periods - for example of the alternating-current period - which are critical for changes in the applied voltage. To that end, the edge zone coating of the film must have a surface conductivity which is less than the surface conductivity of the conductor layer. The only partial charging of the edge zone coating has the result that the potential profile has scarcely any discontinuities and large field strength increases can thus be avoided.