  Suppose that $\{X_t,\,t\ge0\}$ is a non-stationary Markov process, taking
values in a Polish metric space $E$. We prove the law of large numbers and
central limit theorem for an additive functional of the form
$\int_0^T\psi(X_s)ds$, provided that the dual transition probability semigroup,
defined on measures, is strongly contractive in an appropriate Wasserstein
metric. Function $\psi$ is assumed to be Lipschitz on $E$.
