Abstract
In this paper, we give a review of our recent successes in the further development of the density matrix theory to describe the nonequilibrium charge dynamics in semiconductor systems with open electron shells. They are considered two approaches to describe these systems. In the first, systems with a negligibly small spin-orbit coupling are examined, where the description of the electron dynamics is reduced to separate consideration of electrons with different spin directions. If the spin-orbit interaction cannot be neglected, the charge dynamics can be described in the basis of two-component spinors, where spin-flip transitions are allowed. Examples of practical use of the theory in specific cases are given for both methods of description.