We study the evolution of Bianchi-I spacetimes filled with a global unidirectional electromagnetic field F_μν interacting with a massless scalar dilatonic field according to the law Ψ()F^μνF_μν where Ψ() > 0 is an arbitrary function. A qualitative study, among other results, shows that (i) the volume factor always evolves monotonically, (ii) there exist models that become 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 three features are confirmed for exact solutions found for the case usually considered, Ψ = e^2λ, λ = const. In particular, isotropizing models are found for . In the special case |λ| = 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. In the two appendices, we discuss and compare four different isotropization criteria for arbitrary Bianchi-I spacetimes and present their regularity conditions.