  The new method based on the SUSY algebra with supercharges of higher order in
derivatives is proposed to search for dynamical symmetry operators in 2-dim
quantum and classical systems. These symmetry operators arise when closing the
SUSY algebra for a wide set of potentials. In some cases they are of 2-nd order
in derivatives. The particular solutions are obtained also for potentials
accepting symmetry operators of 4-th order. The investigation of quasiclassical
limit of the SUSY algebra yields new classical integrals of motion for a
certain type of systems which are polynomials of 4-th order in momenta. The
general SUSY-inspired algorithm to construct classical systems with additional
integrals of motion is outlined.
