  We give the equations governing the shear evolution in Bianchi spacetimes for
general f(R)-theories of gravity. We consider the case of R^n-gravity and
perform a detailed analysis of the dynamics in Bianchi I cosmologies which
exhibit local rotational symmetry. We find exact solutions and study their
behaviour and stability in terms of the values of the parameter n. In
particular, we found a set of cosmic histories in which the universe is
initially isotropic, then develops shear anisotropies which approaches a
constant value.
