The stability of some classes of systems in standard Bogolyubov form

The stability of the equilibrium of quasilinear systems in standard Bogolyubov form is investigated. Classes of systems are distinguished out for which it is possible to determine the threshold value ɛ0 of the small parameter ɛ which ensures qualitative agreement between the solutions of the initial systems of equations and the solutions of the averaged system corresponding it in an infinite time interval when ɛ < ɛ0.