  The problem of existence and constructing of integrals of motion in
stationary quantum mechanics and its connection with quantum chaoticity is
discussed. It is shown that the earlier suggested quantum chaoticity criterion
characterizes destruction of initial symmetry of regular system and of basis
quantum numbers under influence of perturbation. The convergent procedure
allowing to construct approximate integrals of motion in the form of
non-trivial combinations depending on operators $(q,p)$ is suggested.
Properties of the obtained integrals with complicated structure and the
consequences of their existence for system's dynamics are discussed. The method
is used for explicit construction and investigation of the approximate
integrals in Henon-Heiles problem.
