Epitaxial layers of GaAs on porous Si have been grown at different substrate temperatures T(s) = 200, 300, 400 and 500-degrees-C by molecular beam epitaxy (MBE). The dependence of the surface morphology on the growth conditions has been investigated. The possibility to grow GaAs nano-scale wire crystals with lengths of 5 Am and diameter between 75 and 100 nm has been demonstrated. The optimum temperature for wire growth was found to be 400-degrees-C. We propose two possible mechanisms of growth. The first mechanism we suggest is the anomalous long diffusion length of Ga adatoms on the lateral surface of the growing crystals. For the second mechanism, we suppose the existence of associates and microclusters of Ga and As atoms on the surface semiadsorbtional layer. In this case the crystal growth process can be followed by the vapor-semiadsorptional layer-solid scheme.