  In this paper, we consider two Approximate Deconvolution Magnetohydrodynamics
models which are related to Large Eddy Simulation. We first study existence and
uniqueness of solutions in the double viscous case. Then, we study existence
and uniqueness of solutions of the Approximate Deconvolution MHD model with
magnetic diffusivity, but without kinematic viscosity. In each case, we give
the optimal value of regularizations where we can prove global existence and
uniqueness of the solutions. The second model includes the Approximate
Deconvolution Euler Model as a particular case. Finally, an asymptotic
stability result is shown in the double viscous case with weaker condition on
the regularization parameter.
