  We develop a general setting for N=2 rigid supersymmetric field theories with
gauged central charge in harmonic superspace. We consider those N=2 multiplets
which have a finite number of off-shell components and exist off shell owing to
a non-trivial central charge. This class includes, in particular, the
hypermultiplet with central charge and various versions of the vector-tensor
multiplet. For such theories we present a manifestly supersymmetric universal
action. Chern-Simons couplings to an external N=2 super Yang-Mills multiplet
are given, in harmonic superspace, for both the linear and nonlinear
vector-tensor multiplets with gauged central charge. We show how to deduce the
linear version of the vector-tensor multiplet from six dimensions.
