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 parti
cular, the hypermultiplet with central charge and various versions of the v
ector-tenser multiplet. For such theories we present a manifestly supersymm
etric universal action. Chern-Simons couplings to an external N = 2 super Y
ang-Mills multiplet are given, in harmonic superspace, for both the linear
and non-linear vector-tenser multiplets with gauged central charge. We show
how to deduce the linear version of the vector-tenser multiplet from six d
imensions. (C) 1999 Elsevier Science B.V.