We derive double-dimensional reduction/oxidation in a framework where
it is applicable to describe general nonstatic (and anisotropic) p-bra
ne solutions. Given this procedure, we are able to relate the dynamica
l interaction potential for parallel extremal p-branes in D dimensions
to that for extremal black holes in D - p dimensions. In particular,
we find that to leading order the potential vanishes for all kappa-sym
metric p-branes.