  Until now all known static multi black hole solutions described BPS states
with charges of the same sign. Such solutions could not be related to flat
directions in the space of BPS states. The total number of such states could
not spontaneously increase because of the charge conservation. We show that
there exist static BPS configurations which remain in equilibrium even if they
consist of states with opposite electric (or magnetic) charges from vector
multiplets. This is possible because of the exact cancellation between the
Coulomb and scalar forces. In particular, in the theories with N=4 or N=2
supersymmetry there exist stable massless multi center configurations with
vanishing total charge. Since such configurations have vanishing energy and
charge independently of their number, they can be associated with flat
directions in the space of all possible BPS states. For N=2 case this provides
a realization of the idea that BPS condensates could relate to each other
different vacua of the string theory.
