and the space of matrices 
have
been considered. The existence of such a manifold is sufficient
for multi-frequency oscillations of the system to exist. In
present paper necessary conditions for existence of invariant
tori, the properties of a Green`s operator-function which defines
the main properties of invariant tori of a dynamical system were
considered. The theorem of the existence of invariant torus for
nonlinear matrix system of equations with bilinear main part has
been proved. The method of the iterative construction of this
torus has been obtained.
Key words: dynamical systems, matrix torus, nonlinear oscillations
