  We propose a complete treatment of a local in time dynamics of open quantum
systems. In this approach Markovian evolution turns out to be a special case of
a general non-Markovian one. We provide a general representation of the local
generator which generalizes well known Lindblad representation for the
Markovian dynamics. It shows that the structure of non-Markovian generators is
highly intricate and the problem of their classification is still open. Simple
examples illustrate our approach.
