  Anisotropic stress contributions to the gravitational field can arise from
magnetic fields, collisionless relativistic particles, hydrodynamic shear
viscosity, gravitational waves, skew axion fields in low-energy string
cosmologies, or topological defects. We investigate the effects of such
stresses on cosmological evolution, and in particular on the dissipation of
shear anisotropy. We generalize some previous results that were given for
homogeneous anisotropic universes, by including small inhomogeneity in the
universe. This generalization is facilitated by a covariant approach. We find
that anisotropic stress dominates the evolution of shear, slowing its decay.
The effect is strongest in radiation-dominated universes, where there is slow
logarithmic decay of shear.
