Abstract: Sabin and Catmull-Clark subdivision surfaces are based on the notion of repeated knot insertion of uniform tensor product B-spline surfaces. This paper develops rules for non-uniform Doo-Sabin and Clark surfaces that generalize non-uniform tensor product spline surfaces to arbitrary topologies. This added flexibility allows, among other things, the natural introduction of features such as cusps, creases, and darts, while elsewhere maintaining the same order of tinuity as their uniform counterparts.