A new conduction mechanism in polyethylene and epoxy resin is presented and discussed in this article. This mechanism is based on the presence of charge pulses that can be seen as solitons (solitary waves) crossing dielectrics with mobility 4-5 orders of magnitude larger than that of conventional charge carriers. The nature of this new process that is characterized by charge pulses with such high mobility requires a completely different mechanism for transport to be theorized with respect to that, mediated by trap sites, of conventional charge carriers. It is speculated in this article that injection and transport of positive and negative solitons occurs through the coupling of space charge and relaxation processes involving molecular chains, but of different nature for negative or positive solitons. Observation of space charge shows the existence of such solitons for at least two families of materials, polyethylene, and epoxy resin. In addition, it has been observed that nanostructuration, which is able to modify mechanical properties, affects also the presence and size of the solitons. In this article, we not only seek to demonstrate the existence of this new phenomenon, but attempt to provide an explanation and a kind of qualitative-quantitative model, which shows that the assumption of a pulsive conduction mechanism mediated by chain relaxation processes, transport in free volume (for negative solitons), and reverse-tunneling between macromolecular chains (positive solitons) seems to fit quite well with the experimental observations. (C) 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 49: 1173-1182, 2011