  A discussion is given on possible realization of the Single State Dominance
(SSD) hypothesis in the case of the two-neutrino double beta decay(2nbb-decay)
of 150Nd with 1^- ground state of the intermediate nucleus. We conclude that
the SSD hypothesis is expected to be ruled out by precision measurement of
differential characteristics of this process in running NEMO 3 or planed
SuperNEMO experiments unlike some unknown low-lying 1^+ state of 150Pm does
exist. This problem can be solved via (d,2He) charge-exchange experiment on
150Sm. Further, we address the question about possible violation of the Pauli
exclusion principle for neutrinos and its consequences for the energy
distributions of the 2nbb-decay of 150Nd. This phenomenon might be a subject of
interest of NEMO 3 and SuperNEMO experiments as well.
