  The system of weak normality equations constitutes a part in the complete
system of normality equations. Solutions of each of these two systems of
equations are associated with some definite classes of Newtonian dynamical
systems in Riemannian manifolds. In this paper for the case of simplest flat
Riemannian manifold $M=\Bbb R^n$ with $n\geq 3$ we show that there exist
solutions of weak normality equations that do not solve complete system of
normality equations in whole. Hence associated classes of Newtonian dynamical
systems do not coincide with each other.
