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We examine the behaviour of homogeneous, anisotropic space-times,specifically the locally rotationally symmetric Bianchi types $I$ and $VII_o$in the presence of anisotropic matter. By finding an appropriate constant ofthe motion, and transforming the equations of motion we are able to provideexact solutions in the presence perfect fluids with anisotropic pressures. Thesolution space covers matter consisting of a single perfect fluid whichsatisfies the weak energy condition and is rich enough to contain solutionswhich exhibit behaviour which is qualitatively distinct from the isotropicsector. Thus we find that there is more `matter that matters' close to ahomogeneous singularity than the usual stiff fluid. Example metrics are givenfor cosmologies whose matter sources are magnetic fields, relativisticparticles, cosmic strings and domain walls.

Anisotropic Matter in Cosmology: Locally Rotationally Symmetric Bianchi $I$ and $VII_o$ Models