Recent developments in the theoretical investigation of nuclear double-beta decay are reviewed. In particular, the neutrinoless mode is discussed in detail, since it is sensitive t o lepton number violation as predicted by gauge theories beyond the standard model and it is expected to give important information on the nature of the nenhinos and the weak interaction. Various approximations made in the theoretical treatment of neutrinoless and two-neutrino double beta decay are examined, and the present limits on the effective Majorana mass of the electron neutrino as well as the coupling constants of the right-handed leptonic current are presented.

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