  We consider some aspects of the global evolution problem of Hamiltonian
homogeneous, anisotropic cosmologies derived from a purely quadratic action
functional of the scalar curvature. We show that models can isotropize in the
positive asymptotic direction and that quadratic diagonal Bianchi IX models do
not recollapse and may be regular initially. Although the global existence and
isotropization results we prove hold quite generally, they are applied to
specific Bianchi models in an attempt to describe how certain dynamical
properties uncommon to the general relativity case, become generic features of
these quadratic universes. The question of integrability of the models is also
considered. Our results point to the fact that the more general models are not
integrable in the sense of Painlev\'e and for the Bianchi IX case this may be
connected to the validity of a BKL oscillatory picture on approach to the
singularity in sharp contrast with other higher order gravity theories that
contain an Einstein term and show a monotonic evolution towards the initial
singularity.
