  The mild sufficient conditions for exponential ergodicity of a Markov
process, defined as the solution to SDE with a jump noise, are given. These
conditions include three principal claims: recurrence condition R, topological
irreducibility condition S and non-degeneracy condition N, the latter
formulated in the terms of a certain random subspace of \Re^m, associated with
the initial equation. The examples are given, showing that, in general, none of
three principal claims can be removed without losing ergodicity of the process.
The key point in the approach, developed in the paper, is that the local
Doeblin condition can be derived from N and S via the stratification method and
criterium for the convergence in variations of the family of induced measures
on \Re^m.
