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.

7 pages Revtex