The situation for disk galaxies is more complicated, since the shapes of the dominant modes depend on whether the internal velocities are azimuthally or radially biased. In oblate galaxies with radially-elongated velocity ellipsoids, arguments similar to those given above suggest that an axis ratio of roughly 3:1 is again close to critical, in agreement with N-body simulations for thickened disks. If the stellar velocities are azimuthally biased, the orbits are approximately circular and so the dominant modes are angular (corrugation) modes, δ δ z ∝ ∝ e i m ϕ ϕ . The approximate condition for stability becomes