Stationary axion/dilaton solutions and supersymmetry

We present a new set of supersymmetric stationary solutions of pure N=4,d=4 supergravity 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 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.