  General Lagrangians are constructed for N=2 supersymmetric gauge theories in
four space-time dimensions involving gauge groups with (non-abelian) electric
and magnetic charges. The charges induce a scalar potential, which, when the
charges are regarded as spurionic quantities, is invariant under
electric/magnetic duality. The resulting theories are especially relevant for
supergravity, but details of the extension to local supersymmetry will be
discussed elsewhere. The results include the coupling to hypermultiplets.
Without the latter, it is demonstrated how an off-shell representation can be
constructed based on vector and tensor supermultiplets.
