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We study the possibility that the three mass states of the ordinary activeneutrinos actually split into pairs of quasi-degenerate states, with $\Deltam^2_{kk'} \sim 10^{-12}$ eV$^2$ or less, as a result of mixing of activeneutrinos with sterile neutrinos. Although these quasi-degenerate pairs willlook in laboratory experiment identical to single active states, the CP phasefactors associated with active-sterile mixing might cause cancellations in theeffective electron neutrino mass $m_{ee}$ measured in the neutrinoless doublebeta decay experiments thereby revealing the split nature of states.

CP-phase effects on the effective neutrino mass $m_{ee}$ in the case of quasi-degenerate neutrinos