Gaussian beams generated within astigmatic resonators are themselves astigmatic, having wavefront curvatures and spot sizes that are different when measured in two orthogonal directions. Expressions are derived for the confocal parameters, spot sizes, waist positions, and stability conditions of beams formed within spherical mirror resonators that contain one or more inclined plates (or Brewster-ended laser rods). An expression is also derived for the resonant frequencies of the TEMmnmode in such a resonator. It is shown that the frequency degeneracy between modes of the same is lifted and the frequency splittings are calculated. The astigmatism produced by prisms used for dispersion is also considered and precautions are described for avoiding serious astigmatism in resonators containing such prisms.