Dynamics of a Self–gravitating Magnetized Source. Received Day Month Year Revised Day Month Year Communicated by Managing Editor

We consider a magnetized degenerate gas of fermions as the matter source of a homogeneous but anisotropic Bianchi I spacetime with a Kasner–like metric. We examine the dynamics of this system by means of a qualitative and numerical study of Einstein-Maxwell field equations which reduce to a non–linear autonomous system. For all initial conditions and combinations of free parameters the gas evolves from an initial anisotropic singularity into an asymptotic state that is completely determined by a stable attractor. Depending on the initial conditions the anisotropic singularity is of the " cigar " or " plate " types.