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.
