The paper deals with the investigations of the discharge in hydrogen in the conditions close to that for the trigger units of the pseudospark switches. The following modes of discharge sustaining are classified: the Townsend discharge, the suppressed glow discharge with hollow cathode, the intermediate mode of the gradual transition from the suppressed discharge to the ordinary glow discharge, and the ordinary discharge in which the negative glow plasma occupies the whole depth of the cathode cavity. As applied to the ordinary discharge, the theoretical model that offers a possibility to estimate the negative glow parameters is developed. In the current range (1.6–10) mA the electron densities in the negative glow region are (1.7–8.7) 108cm–3. The interpretation for the mechanism of the current passage to the anode is also proposed based on the model. In particular, the explanation of the fact that at a low discharge current the region of the positive column plasma near the flat anode appears is given.