  We compute the first-order $\alpha'$ corrections to well-known families of
heterotic multi-center black-hole solutions in five and four dimensions. The
solutions can be either supersymmetric or non-supersymmetric, depending on the
relative sign between two of the black-hole charges. For both cases, we find
that the equilibrium of forces persists after including the $\alpha'$
corrections, as the existence of multi-center solutions free of unphysical
singularities shows. We analyze the possibility of black-hole fragmentation.
