For vitreous selenium films, from 5 to 57 μm in thickness, dark steady‐state current—voltage characteristics are measured between 1 and 103V. The currents proportional to U2 d−3 can be interpreted in terms of space‐charge‐limited currents (SCLC) with a single trap level. A steep increase in current at the end of the square‐law region is not caused by trap filling but by field ionization. The mean value of the electric field at the cathode, at which the ionization current predominates over the SCLC is of the order of 1.3 × 107Vm−1. Restrictions imposed on SCLC by the field ionization of traps are discussed. Copyright © 1968 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim