  We present a class of exact cosmological solutions of the low energy string
effective action in the presence of a homogeneous magnetic fields. We discuss
the physical properties of the obtained (fully anisotropic) cosmologies paying
particular attention to their vacuum limit and to the possible isotropization
mechanisms. We argue that quadratic curvature corrections are able to
isotropize fully anisotropic solutions whose scale factors describe accelerated
expansion. Moreover, the degree of isotropization grows with the duration of
the string phase. We follow the fate of the shear parameter in a decelerated
phase where, dilaton, magnetic fields and radiation fluid are simultaneously
present. In the absence of any magnetic field a long string phase immediately
followed by radiation is able to erase large anisotropies. Conversely, if a
short string phase is followed by a long dilaton dominated phase the
anisotropies can be present, in principle, also at later times. The presence of
magnetic seeds after the end of the string phase can induce further
anisotropies which can be studied within the formalism reported in this paper.
