In automobiles, for example, the exhaust fumes must pass through a plasma reactor operating by the principle of dielectrically inhibited ("silent") discharge, consisting of an arrangement of flat plates with alternating metallic and dielectric layers, whereby a plurality of adjacent discharge paths in parallel in the flow direction are formed. According to the invention, the discharge paths border on a single metallic electrode surface or layer (62, 72) and the electric power is supplied (58, 59) from two different sides with the metallic layers (62, 72) having alternating polarities.