(eng): This contribution addresses a possible description of the chaotic behavior in multi-valued dynamical systems. An important area leading to description via the multi-valued dynamical systems is the non-smooth dynamical systems theory and their applications. Examples of such applications are mechanics with dry friction, electric circuits with small conductivity, systems with small inertia, economy, biology, control theory, game theory, optimization, etc. The phenomenon of the chaos in multi-valued systems is even more complicated issue than in case of the single-valued ones and deserves to be intensively studied. The most of the existing results proves the existence of chaos in multi-valued systems via an appropriate construction of a homeomorphism between one selected solution from the set of them and the bi-directional full shift of symbols. The approach presented here does not require construction of a selector on the set of solutions and uses a more intuitive and descriptive definition of the chaos.