A review is given of theoretical work performed in connection with a new approach to the theory of a weakly turbulent plasma. The essence of this approach is the representation of turbulent plasma as an aggregate of weakly interacting gases of particles (ions, electrons) and quasi-particles (collective oscillations). In such a scheme are included also instability effects (playing the role of sources in the kinetic equations for quasi-particles). As applications of this method, which is thus a generalization of the known quasi-linear theory, some anomalous transfer phenomena that appear as the result of different types of plasma instability have been discussed.
Theory of interaction between particles and waves with a non-equilibrium plasma