Abstract. Theory of Markov (or manyvaled) maps or polymorphisms 
can be considered as extension of ergodic theory and deterministic 
dynamics. The most of interest and new effect here is the exsitence 
of the polymorphisms which are nondeterministic perturbations of 
K-(or hyperbolic) systems and in the same time, are quasisimilar 
to unperturbed deterministic systems. These are very special as 
random perturbations, however as polymorphisms they are generic.