The shadowing problem is related to the following question: under which condition, for any pseudotrajectory approximate trajectory) of a vector field there exists a close trajectory? It is known that in a neighbourhood of a hyperbolic set diffeomorphisms and vector fields have shadowing property. In fact more general statement is correct: structurally stable dynamical systems satisfy shadowing property.

We are interested if converse implication is correct. We consider notion of Lipschitz shadowing property and proved that it is equivalent to structural stability for the cases of diffeomorphisms and vector fields.

Talk is based on joint works with S. Pilyugin and K. Palmer