  The gravitini zero modes riding on top of the extreme Reissner-Nordstrom
black-hole solution of N=2 supergravity are shown to be normalizable. The
gravitini and dilatini zero modes of axion-dilaton extreme black-hole solutions
of N=4 supergravity are also given and found to have finite norms. These norms
are duality invariant. The finiteness and positivity of the norms in both cases
are found to be correlated with the Witten-Israel-Nester construction; however,
we have replaced the Witten condition by the pure-spin-3/2 constraint on the
gravitini. We compare our calculation of the norms with the calculations which
provide the moduli space metric for extreme black holes.
  The action of the N=2 hypermultiplet with an off-shell central charge
describes the solitons of N=2 supergravity. This action, in the
Majumdar-Papapetrou multi-black-hole background, is shown to be N=2 rigidly
supersymmetric.
