The α2-dynamo of Hollerbach and Ierley (1991) is converted into an αω-dynamo, and the analysis of Barenghi and Jones (1991) is extended. Only one choice of α and ω is considered in detail, for both negative and positive dynamo numbers. The solutions in the viscously limited regime are qualitatively distinct, with negativeDsolutions oscillating about a zero mean, and positiveDsolutions oscillating about a non-zero mean. The existence of nonlinear eigenvaluesDxis demonstrated, beyond which the solutions are no longer viscously limited. The subsequent evolution would appear to be independent of the viscosity in some average sense, but there is no evidence of a true Taylor state.