Models of spherical dynamos are considered which involve the full interaction between the magnetic field and the motion of an incompressible conducting fluid. In the basic equations magnetic field and fluid velocity are expanded in series of certain decay modes. In this way these equations are reduced to an infinite set of ordinary first-order differential equations for the coefficients of these expansions. The behaviour of dynamos can then be studied by integrating a finite set of these equations numerically. Some first results obtained in this way are presented for mean-field models in which the growth of the magnetic field due to the α–effect is limited by large-scale motions generated by Lorentz forces.