[en] A theoretical description of electron transmission through a molecular wire embedded in between two leads is carried out using the density matrix method. Accounting for the Coulomb repulsion among the transferred electrons nonlinear kinetic equations for the reduced single-electron distributions are derived. The respective transfer rates contain contributions from different transmission channels which are characterized by the number of excess electrons present in the wire in the course of the charge transmission. Special attention is focused on the study of single-electron transmission. It is shown that a direct lead-lead (elastic) transmission as well as a transmission including the population of intermediate wire states (inelastic transmission) becomes possible if the electron to be transferred moves through a wire without a further excess charge. The probability to find a molecule in such an 'empty' wire state follows from a relation between the rates of incoming and outgoing lead-molecule/molecule-lead charge transfer. In turn, they are responsible for the formation of the inelastic component of the current. Thus, it could be demonstrated that the inelastic charge transmission not only determines the inelastic part of the current but is able to control the elastic component as well. Moreover, the inelastic transmission may result in a specific kinetic rectification effect