resolved within the indicated period. We will also assume that by 2010 one or more -decay experiments of the next generation will be operative, and that at least the physical range of variation of the values of the relevant -decay nuclear matrix elements will be unambiguously determined. Since all discussed future experiments (except the 10 ton version of GENIUS [@GENIUS]) have a sensitivity to ${\mbox{$\left|  < \! m  \! > \right| \ $}}\!\! > 0.01$ eV, while in the case of NH neutrino mass spectrum is predicted to be smaller than 0.01 eV, we will not consider the possibility of finding CP-violation for the NH spectrum (for a discussion of this possibility see, e.g., [@PPW; @WR0302]).

We begin with a general analysis the aim of which is to determine what is the maximal uncertainty in the value of due to the imprecise knowledge of the corresponding nuclear matrix elements, which might still allow one to find CP-violation associated with Majorana neutrinos. This is followed by results on the problem of finding the CP-violation of interest, derived by a simplified error analysis of prospective input data on $m_{\bar{\nu}_e}$ or $\Sigma$, $\tan^2\theta_{\odot}$, $\!\!$, etc. The effects of the nuclear matrix element uncertainty 