In this article we define and build the one method of description of stochastic evolution of a physical quantum system. For each quantum state w∈E_U we construct the probability measure u_w in the space (P_U, S), where P_U is the space of the pure states of the quantum system, S the Borel σ-algebra in P_U. Farther, for any Hermit's positive element with norm ‖u‖=1, in the C*-algebra of observables U, we define the probability measure u_u on the set of states E_U. If strongly continuous group ｛α_t｝of * automorphisms on U describes the evolution of structure of observables, according to this, we have a picture of evolution of distribution of states of quantum system relatively to each observable u.