Аннотация:The author extends a theorem of Tikhonov for singularly perturbed systems. In the original theorem, the main condition of passing singularly perturbed systems to degenerate systems is related to the asymptotic stability of the equilibrium position of an associated system. In the presented theorem the condition of asymptotic stability of the associated system is replaced by the condition of marginal stability under the additional assumption that the derivate of its Lyapunov function has a negative mean by virtue of the singularly perturbed system. The theorem is well defined and proven in detail. The presented theorem weakens the condition of asymptotic stability. However, the mean of the Lyapunov function has to be found from the solution of an averaged system. Thus, the practical application of the theorem is more complicated.