  We present dyonic BPS static black hole solutions for general d=4, N=2
supergravity theories coupled to vector and hypermultiplets. These solutions
are generalisations of the spherically symmetric Majumdar-Papapetrou black hole
solutions of Einstein-Maxwell gravity and are completely characterised by a set
of constrained harmonic functions. In terms of the underlying special geometry,
these harmonic functions are identified with the imaginary part of the
holomorphic sections defining the special K\"ahler manifold and the metric is
expressed in terms of the symplectic invariant K\"ahler potential. The
relations of the holomorphic sections to the harmonic functions constitute the
generalised stabilisation equations for the moduli fields. In addition to
asymptotic flatness, the harmonic functions are also constrained by the
requirement that the K\"ahler connection of the underlying Hodge-K\"ahler
manifold has to vanish in order to obtain static solutions. The behaviour of
these solutions near the horizon is also explained.
