  We give the global picture of the normalized Ricci flow on generalized flag
manifolds with two or three isotropy summands. The normalized Ricci flow for
these spaces descents to a parameter depending system of two or three ordinary
differential equations, respectively. We present here the qualitative study of
these system's global phase portrait, by using techniques of Dynamical Systems
theory. This study allows us to draw conclusions about the existence and the
analytical form of invariant Einstein metrics on such manifolds, and seems to
offer a better insight to the classification problem of invariant Einstein
metrics on compact homogeneous spaces.
