  The problem is considered of describing the dynamics of quantum systems
generated by a nonlocal in time interaction. It is shown that the use of the
Feynman approach to quantum theory in combination with the canonical approach
allows one to extend quantum dynamics to describe the time evolution in the
case of such interactions. In this way, using only the current concepts of
quantum theory, a generalized equation of motion for state vectors is derived.
In the case, where the fundamental interaction generating the dynamics in a
system is local in time, this equation is equivalent to the Schr{\"o}dinger
equation. Explicit examples are given for an exactly solvable model. The
proposed formalism is shown to provide a new insight into the problem of the
description of nonlocal interactions in quantum field theory. It is shown that
such a property of the equation of motion as nonlocality in time may be
important for describing hadron-hadron interactions at low and intermediate
energies.
