  The motion of charged test-particles in the gravitational field of a rotating
and electromagnetically charged black hole as described by the Kerr-Newman
metric is considered. We completely classify the colatitudinal and radial
motion on the extended manifold $-\infty \leq r \leq \infty$, including orbits
crossing the horizons or $r=0$. Analytical solutions of the equations of motion
in terms of elliptic functions are presented which are valid for all types of
orbits.
