Braginskii’s theory of nearly axisymmetric dynamo action, as reinterpreted by Soward, is presented. The departure from axisymmetry is what allows Cowling’s anti-dynamo theorem to be bypassed. A Lagrangian transformation of the induction equation leads first to a natural interpretation of Braginskii’s ‘effective variables’ and second to an axisymmetric mean-field equation in which a regenerative dynamo term appears that is wholly diffusive in origin, resulting from a diffusive phase shift between velocity and magnetic perturbation fields. This regenerative term is again associated with chirality in the perturbation velocity field. In the geomagnetic context, matching conditions to the external poloidal field are obtained, and the secular variation of the external field admits interpretation in terms of the fluctuating part of this external field. Soward’s theory involves hybrid Euler–Lagrange techniques, which also arise in the theory of the interaction between waves and mean flows on which they may be superposed.