  We consider generic i.e., forming an everywhere dense massive subset classes
of Markov operators in the space $L^2(X,\mu)$ with a finite continuous measure.
Since there is a canonical correspondence that associates with each Markov
operator a multivalued measure-preserving transformation (i.e., a
polymorphism), as well as a stationary Markov chain, we can also speak about
generic polymorphisms and generic Markov chains. The most important and
inexpected generic properties of Markov operators (or Markov chains or
polymorphisms) is nonmixing and totally nondeterministicity. It was not known
even existence of such Markov operators (the first example due to
M.Rozenblatt). We suppose that this class coinsided with the class of special
random perturbations of $K$-automorphisms. This theory is measure theoretic
counterpart of the theory of nonselfadjoint contractions and its application.
