Abstract
The quantisation procedure in the harmonic superspace approach is worked out. Harmonic distributions are introduced and are used to construct the analytic superspace delta functions and the Green functions for the hypermultiplet and the N=2 Yang-Mills superfields. The gauge fixing is described and the relevant Faddeev-Popov ghosts are defined. The corresponding BRST transformations are found. The harmonic superspace quantisation of the N=2 gauge theory turns out to be rather simple and has many parallels with that for the standard (N=0) Yang-Mills theory. In particular, no ghosts-for-ghosts are needed.
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