The nature of internal discharges in actual insulation and also on model circuits exposed to alternating voltages is studied by means of a special oscillographic bridge equipment. A theory of the occurrence of these discharges is developed and is shown to agree with the oscillographic observations and to give correctly the effect of varying different conditions. Examples of the different kinds of phenomena which may occur are given, illustrating the qualitative and, in some instances, quantitative application of the theory. It is shown that, with alternating voltages, discharges, once initiated, can continue at a much lower voltage than that which corresponds to the critical or ignition stress in the dielectric.