  Theoretical foundation and application of the generalized spin-fermion (sp-d)
exchange lattice model to magnetic and diluted magnetic semiconductors are
discussed. The capabilities of the model to describe spin quasi-particle
spectra are investigated. The main emphasis is made on the dynamic behavior of
two interacting subsystems, the localized spins and spin density of itinerant
carriers. A nonperturbative many-body approach, the Irreducible Green Functions
(IGF) method, is used to describe the quasi-particle dynamics. Scattering
states are investigated and three branches of magnetic excitations are
calculated in the regime, characteristic of a magnetic semiconductor. For a
simplified version of the model (Kondo lattice model) we study the spectra of
quasi-particle excitations with special attention given to diluted magnetic
semiconductors. For this, to include the effects of disorder, modified mean
fields are determined self-consistently. The role of the Coulomb correlation
and exchange is clarified by comparing of both the cases.
