Abstract: For a given rotation-invariant operator Ω in the unit disc, the necessary condition for thef xistence of finite invariant measures of the strong Markov transition functions determined by Ω with the Ventzel's boundary conditions of finite rank is established If only rotation-invariant transition functions are considered, then the necessary and sufficient conditions for a given measure to be invariant and to be reversible, and all the corresponding boundary conditions for posseusiug these properties have been found explicitly in this paper.