  We consider the asymptotic behavior of the normalized Ricci flow on
generalized Wallach spaces that could be considered as special planar dynamical
systems. All non symmetric generalized Wallach spaces can be naturally
parametrized by three positive numbers $a_1, a_2, a_3$. Our interest is to
determine the type of singularity of all singular points of the normalized
Ricci flow on all such spaces. Our main result gives a qualitative answer for
almost all points $(a_1,a_2,a_3)$ in the cube $(0,1/2]\times (0,1/2]\times
(0,1/2]$.
