The structure of the near-electrode regions of a thermoelectronic laser energy converter filled with a two-component gas mixture (noble gas + easily ionized additive) is investigated under conditions such that the main gas near the electrodes is weakly ionized. Specific features of the distributions of the densities of the main-gas ions and the ions and atoms of the additive, the temperature of the heavy plasma components, and the electric potential near the electrodes are examined at different total densities of the atoms and ions of the additive. The boundary conditions are determined at the near-electrode boundaries of the equilibrium core of a continuous optical discharge in a thermoelectronic laser energy converter filled with a two-component gas mixture.