When thin films of polar plastic materials are subjected to d.c. potentials of 10 to 300 volts per mil they exhibit current fluctuations (with frequencies in the range of 60 to 1000 c.p.s.) which last for minutes and which even persist for a few seconds on removing the voltage. These fluctuations are about 1000 fold above the noise level of the circuit and are about 1 percent of the steady d.c. current. They eventually die out but can usually be restored by reversing the polarity. This noise is greater the more polar the nature of the polymer and the higher its moisture content. The effect seems to arise from water or impurity ions which can jump whenever a hole opens between polymer chains and is thus an activated rate process sufficiently slowed down by the highly viscous nature of the polymeric medium to be readily observable. On an oscillograph screen it is possible to see both the forward and the backward diffusion. This noise is most pronounced in Cellophane, Nylon, and copolymers of vinylidene chloride with acrylonitrile, but also appears with polystyrene stored at 86 percent relative humidity. Films of methylcellulose do not show the effect. Numerically the effect seems to arise from the random motion of groups of several hundred ions as a unit. As an extension of these ideas it is suggested and demonstrated that the moisture vapor diffusion constants for a series of polymers increase with the frequency of the loss factor maximum while the moisture vapor permeability increases with the direct current conductivity.