  The global properties of spatially homogeneous cosmological models with
collisionless matter are studied. It is shown that as long as the mean
curvature of the hypersurfaces of homogeneity remains finite no singularity can
occur in finite proper time as measured by observers whose worldlines are
orthogonal to these hypersurfaces. Strong cosmic censorship is then proved for
the Bianchi I, Bianchi IX and Kantowski-Sachs symmetry classes.
