  I consider the problem of weakly nonlinear stability of three-dimensional
parity-invariant magnetohydrodynamic systems to perturbations, involving large
scales. I assume that the MHD state, 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 MHD state. Mean-field
equations, which I derive for the perturbation using asymptotic techniques for
multiscale systems, are a generalization of the standard equations of
magnetohydrodynamics (the Navier-Stokes equation with the Lorentz force and the
magnetic induction equation). In them, the operator of combined eddy
diffusivity emerges, which is in general anisotropic and not necessarily
negatively defined, and new quadratic terms, analogous to the ones describing
advection. A method for efficient computation of coefficients of the eddy
diffusivity tensor and eddy advection terms in the mean-field equations is
proposed.
