The paper deals with a spherical mean-field dynamo model of α2-type in which the back-reaction of the magnetic field on the fluid motion is taken into account by a dependence of the α-coefficient on either the total magnetic energy or the local magnetic energy density. Results of some experiments are presented which have been carried out with a numerical code that follows the evolution of the magnetic field. Particular attention is paid to steady fields and their stability. It is stressed that the results of stability analyses restricted to axisymmetric perturbations crucially differ from those that also include non-axisymmetric perturbations.