  We consider two Large Eddy Simulation (LES) models for the approximation of
large scales of the equations of Magnetohydrodynamics (MHD in the sequel). We
study two $\alpha$-models, which are obtained adapting to the MHD the approach
by Stolz and Adams with van Cittert approximate deconvolution operators. First,
we prove existence and uniqueness of a regular weak solution for a system with
filtering and deconvolution in both equations. Then we study the behavior of
solutions as the deconvolution parameter goes to infinity. The main result of
this paper is the convergence to a solution of the filtered MHD equations. In
the final section we study also the problem with filtering acting only on the
velocity equation.
