The observed westward drift of some patches of the Earth's magnetic field suggests that the geodynamo is of the αω kind. However solutions of the αω dynamo equations tend to oscillate on a very rapid time scale, in disagreement with the observed long times between reversals. It is suggested that the problem can be cured by taking into account the generation of toroidal field by the α effect. The resulting α2ω dynamo equations are solved in the geometry of a spherical shell in both the linear and the nonlinear regime. Steady and oscillatory Taylor state solutions are found. The slow time dependence of the oscillatory solutions compares well with the observed frequency of geomagnetic reversals.