  We derive double dimensional reduction/oxidation in a framework where it is
applicable to describe general non-static (and anisotropic) $p$-brane
solutions. Given this procedure, we are able to relate the dynamical
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 $\kappa$-symmetric $p$-branes.
