  We study Bianchi I type brane cosmologies with scalar matter self-interacting
through combinations of exponential potentials. Such models correspond in some
cases to inflationary universes. We discuss the conditions for accelerated
expansion to occur, and pay particular attention to the influence of extra
dimensions and anisotropy. Our results show that the associated effects evolve
in such a way that they become negligible in the late time limit, those related
to the anisotropy disappearing earlier. This study focuses mainly on single
field models, but we also consider a generalization yielding models with
multiple non-interacting fields and examine its features briefly. We conclude
that in the brane scenario, as happens in general relativity, an increase in
the number of fields assists inflation.
