  New generation experiments on search for neutrinoless double beta decay with
sensitivity to effective Majorana neutrino mass on the level $\sim$ 3-5 meV is
discussed. Possible restrictions at achievement of this purpose (possibility to
produce big amount of enriched isotopes, possibility to reach very low
background level, energy resolution and possible cost of experiments) are
considered. It is shown that for realization of so ambitious project 10 tons
(or more) of enriched isotope is required. Background index should be on the
level $\le$ 10$^{-5}-10^{-6}$ c/kg$\cdot$ keV$\cdot$ y. Besides, the energy
resolution of the detector should be not worse than 1-2%. It is shown that
$^{130}$TeO$_2$ low temperature bolometer looks as the most realistic candidate
for such experiments. Under some conditions experiments with $^{76}$Ge,
$^{100}$Mo and $^{136}$Xe can be realized too.
