  As a step toward constructing realistic brane world models in string theory,
we consider the interactions of a pair of non-BPS branes. We construct a dyonic
generalization of the non-BPS branes first constructed by Bergman, Gaberdiel
and Sen as orbifolds of D-branes on $T^4/\BZ_2$. The force between a dyonic
brane and an electric brane is computed and is found to vanish at a nontrivial
critical separation. This equilibrium point is unstable. For smaller
separations the branes coalesce to form a composite dyonic state, while for
larger separations the branes run off to infinity. We suggest generalizations
that will lead to potentials with stable local minima.
