According to the existing modified electrode theory, both radical-cations (polarons) and reduced quasi-particles of conducting polymer films include the same number of repeat units of polymer chains. As opposed to such supposition, any reduced repeat unit of polymer chains is assumed to be a separate quasiparticle in scope of the recently proposed approach to treating the conductance of polaron-containing films. To say nothing of the obtained new results of such approach, it is necessary to indicate that its applications have been restricted so far to the cases of either a homogeneous polaron population, which means the absence of any polaron transformations (for example, into bipolarons), or the presence of such transformations proceeding in equilibrium conditions. The main purpose of the presented communication is to derive charge carrier fluxes and material balance equations valid for non-equilibrium conditions and accounting for the above transformations and translocations of quasi-particles along polymer chains. Consecutive acts of any type of the indicated processes are treated as sequences of similar reactions proceeding in the film interior. This allows one to apply the Brönsted rule of linear correlation between activation energies of such reactions and their generalized heat effects, in order to express the reaction rate as a function of the local electric field. Using a lattice model of films formed by unramified polymer chains, non-stationary flux and material balance equations have been obtained. A comparison between the derived results and those conformed to the existing theory shows their significant difference. Some other inferences from the description carried out and possible prospects of its development are discussed.