Skobeltsyn Institute of Nuclear Physics
Lomonosov Moscow State University

A Quasi-classical model in SU(N) gauge theory is developed. Selfconsistent solutions of inhomogenous Yang-Mills equation and Dirac equation in external field are found with Yang-Mills fields in the eikonal form. Quantization of
the solutions is performed in the quasi-classical approximation. It is shown, that selfconsistent solutions do exist for dimension of the gauge N = 3 or N> 3. In this case fermion current and gauge field current compensate each other. The solutions being obtained are applied to QCD in view of a study of multiple fermion states in QGM and of hadronisation process.