  We study the evolution of Bianchi-I space-times filled with a global
unidirectional electromagnetic field $F_{mn}$ interacting with a massless
scalar dilatonic field according to the law \Psi(\phi) F^{mn} F_{mn} where
\Psi(\phi) > 0 is an arbitrary function. A qualitative study, among other
results, shows that (i) the volume factor always evolves monotonically, (ii)
there exist models becoming isotropic at late times and (iii) the expansion
generically starts from a singularity but there can be special models starting
from a Killing horizon preceded by a static stage. All these features are
confirmed for exact solutions found for the usually considered case \Psi =
e^{2\lambda\phi}, \lambda = const. In particular, isotropizing models are found
for |\lambda| > 1/\sqrt{3}. In the special case |\lambda| = 1, which
corresponds to models of string origin, the string metric behaviour is studied
and shown to be qualitatively similar to that of the Einstein frame metric.
