The stability of nonlinear mean-field dynamo models in spherical geometry has been investigated numerically. Assuming axisymmetry and incompressibility we find stable stationary solutions of both even and odd parity over a range of four decades in the Taylor number. Furthermore, we extend studies on solutions with “mixed parity”, which have been found previously for an αω-dynamo model, neglecting here, however, the explicit feedback on the mean motions. Plots of trajectories in phase space and Poincaré maps, showing intersections of the trajectories with certain hyperplanes in phase space, reveal that the solution lies on a torus for some of these models.