  We present two new classes of dyonic anti-de Sitter black hole solutions of
4-dimensional maximal N=8, SO(8) gauged supergravity. They are: (1) static
black holes of N=2, U(1)^4 gauged supergravity with 4 electric and 4 magnetic
charges, with spherical, planar or hyperbolic horizons; and (2) rotating black
holes of N=2, U(1)^2 gauged supergravity with 2 electric and 2 magnetic
charges. We study their thermodynamics, and point out that the formulation of a
consistent thermodynamics for dyonic anti-de Sitter black holes is dependent on
the existence of boundary conditions for the gauge fields. We identify several
distinct classes of boundary conditions for gauge fields in U(1)^4
supergravity. We study a general family of metrics containing the rotating
solutions, and find Killing-Yano tensors with torsion in two conformal frames,
which underlie separability.
