  The description of invariants of surfaces with respect to the motion groups
is reduced to the description of invariants of parameterized surfaces with
respect to the motion groups. Existence of a commuting system of invariant
partial differential operators (derivatives) and a finite system of invariants,
such that any invariant of the surface is a function of these invariants and
their invariant derivatives, is shown. The offered method is applicable in more
general settings than the "Moving Frame Method" does in differential geometry.
