  We derive in this preprint the moment and exponential tail estimates,
sufficient conditions for the Non-Central Limit Theorem (NCLT) in the ordinary
one-dimensional space as well as in the space of continuous functions for the
properly (natural) normalized multi-indexed sums of function of random
variables, processes or fields (r.f.), on the other words V-statistics,
parametric, in general case.
  We construct also some examples in order to show the exactness of obtained
estimates.
  We will use the theory of the so-called degenerate approximation of the
functions of several variables as well as the theory of
  Grand Lebesgue Spaces (GLS) of measurable functions (random variables).
