  In this paper, we investigate Murre's conjecture on the existence of a
Chow--Kuenneth decomposition for a rational homogeneous bundle $Z\to S$ over a
smooth variety, defined over complex numbers. Chow-K\"unneth decomposition is
exhibited for $Z$ whenever $S$ has a Chow--Kuenneth decomposition. The same
conclusion holds for a class of log homogeneous varieties, studied by M. Brion.
