We obtain exact solutions for the Einstein equations with an exponential-potential scalar field (\(V=��e^{k��}\)) which represent simple inhomogeneous generalizations of Bianchi I cosmologies. Studying these equations numerically we find that in most of the cases there is a certain period of inflationary behaviour for \(k^2<2\). We as well find that for \(k^2>2\) the solutions homogenize generically at late times. Yet, {\em none of the solutions} isotropize. For some particular values of the integration constants we find a multiple inflationary behaviour for which the deceleration and the inflationary phases interchange each other several times during the history of the model.

18 pages, Plain LaTeX, 2 Figures to be sent on request, to appear in Phys. Rev. D., report 2