  I consider the problem of weakly nonlinear stability of three-dimensional
convective magnetohydrodynamic systems, where there is no alpha-effect or it is
insignificant, to perturbations involving large scales. I assume that the
convective MHD state (steady or evolutionary), the stability of which I
investigate, does not involve large spatio-temporal scales, and it is stable to
perturbations involving the same small spatial scales, as the perturbed state.
Mean-field equations, which I derive for the perturbation using asymptotic
techniques for multiscale systems, are a generalization of the equations of
magnetohydrodynamics (the Navier-Stokes and magnetic induction equations). The
operator of combined eddy diffusivity emerges, which is in general anisotropic
and not necessarily negatively defined, as well as new quadratic terms
analogous to the ones describing advection.
