  Extended Einstein-Maxwell model and its application to the problem of
evolution of magnetized Bianchi-I Universe are considered. The evolution of
medium magnetization is governed by a relaxation type extended constitutive
equation. The series of exact solutions to the extended master equations is
obtained and discussed. The anisotropic expansion of the Bianchi-I Universe is
shown to become non-monotonic (accelerated/decelerated) in both principal
directions (along the magnetic field and orthogonal to it). A specific type of
expansion, the so-called evolution with hidden magnetic field, is shown to
appear when the magnetization effectively screens the magnetic field and the
latter disappears from the equations for gravitational field.
