N=2 massive gauge superfields in harmonic superspace

The Higgs mechanism of extended supersymmetry is formulated in a N=2 superfield language. It is shown explicitly how an N=2 gauge superfield can acquire a mass, and a spin-1 gauge boson, 4 spin-1/2 inos and 5 spin-0 Higgs bosons are described. Moreover the global SU(2) invariance group which acts on the two supersymmetry generators may be preserved, if one uses systematically pairs of Higgs hypermultiplets - as done earlier in the construction of N=2 supersymmetric GUTs - each pair being described by an ω-type analytic superfield. (orig.)