  It is shown that the Majorana nature of the heavy neutrinos $N_j$ having
masses in the range of $M_j \sim (100 - 1000)$ GeV and present in the TeV scale
type I and inverse see-saw scenarios of neutrino mass generation, is unlikely
to be observable in the currently operating and future planned accelerator
experiments (including LHC) due to the existence of very strong constraints on
the parameters and couplings responsible for the corresponding $|\Delta L| = 2$
processes, $L$ being the total lepton charge. If the heavy Majorana neutrinos
$N_j$ are observed and they are associated only with the type I or inverse
see-saw mechanisms and no additional TeV scale "new physics", they will behave
like Dirac fermions to a relatively high level of precision, being actually
pseudo-Dirac particles. The observation of effects proving the Majorana nature
of $N_j$ would imply that these heavy neutrinos have additional relatively
strong couplings to the Standard Model particles (as, e.g. in the type III
see-saw scenario), or that light neutrino masses compatible with the
observations are generated by a mechanism other than see-saw (e.g., radiatively
at one or two loop level) in which the heavy Majorana neutrinos $N_j$ are
nevertheless involved.
