  We consider the Ricci flow equation for invariant metrics on compact and
connected homogeneous spaces whose isotropy representation decomposes into two
irreducible inequivalent summands. By studying the corresponding dynamical
system, we completely describe the behaviour of the homogeneous Ricci flow on
this kind of spaces. Moreover, we investigate the existence of ancient
solutions and relate this to the existence and non-existence of invariant
Einstein metrics.
