  The quasi-classical model in a gauge theory with the Yang-Mills (YM) field is
developed. On a basis of the exact solution of the Dirac equation in the SU(N)
gauge field, which is in the eikonal approximation, the Yang-Mills (YM)
equations containing the external fermion current are solved. The derived
solutions are quantized in the quasi-classical approach. The developed model
proves to have the self-consistent solutions of the Dirac and Yang-Mills
equations at $N\geq 3$. Thereat the solutions take place provided that the
fermion and gauge fields exist simultaneously, so that the fermion current
completely compensates the current generated by the gauge field due to it
self-interaction. The obtained solution are considered in the context of QCD.
