  The dynamical systems of the form $\ddot\bold r=\bold F (\bold r,\dot\bold
r)$ in $\Bbb R^n$ accepting the normal shift are considered. The concept of
weak normality for them is introduced. The partial differential equations for
the force field $\bold F(\bold r,\dot\bold r)$ of the dynamical systems with
weak and complete normality are derived.
