  We present a new set of supersymmetric stationary solutions of pure N=4,d=4
supergravity (and, hence, of low-energy effective string theory) that
generalize (and include) the Israel-Wilson-Perj\'es solutions of
Einstein-Maxwell theory. All solutions have 1/4 of the supersymmetries unbroken
and some have 1/2. The full solution is determined by two arbitrary complex
harmonic functions {\cal H}_{1,2} which transform as a doublet under SL(2,\R) S
duality and N complex constants k^{(n)} that transform as an SO(N) vector. This
set of solutions is, then, manifestly duality invariant. When the harmonic
functions are chosen to have only one pole, all the general resulting
point-like objects have supersymmetric rotating asymptotically Taub-NUT metrics
with 1/2 or 1/4 of the supersymmetries unbroken. The static, asymptotically
flat metrics describe supersymmetric extreme black holes. Only those breaking
3/4 of the supersymmetries have regular horizons. The stationary asymptotically
flat metrics do not describe black holes when the angular momentum does not
vanish, even in the case in which 3/4 of the supersymmetries are broken.
