  One unusual property of dynamic systems, whose state is characterized by a
set of scalar dynamic variables satisfying a system of differential equations
of a general form, is considered. This property is related to the behavior of
equations (optionally covariant) with respect to coordinate diffeomorphisms:
the equations, in a sense, retain their form on their solutions. More
precisely, non-covariant addends to the equations of such systems always
exactly reduced in any order of perturbation theory by solutions of unperturbed
(initial) equations. This property demonstrated by a set of simple illustrative
examples. Various aspects of the dynamic covariance are discussed.
