  We study asymptotical probabilities of first order and monadic second order
properties of Erdos-Renyi random graph G(n,n^{-a}). The random graph obeys FO
(MSO) zero-one k-law if for any first order (monadic second order) formulae it
is true for G(n,n^{-a}) with probability tending to 0 or to 1. Zero-one k-laws
are well studied only for the first order language and a < 1. We obtain new
zero-one k-laws (both for first order and monadic second order languages) when
a > 1. Proofs of these results are based on the existed study of first order
equivalence classes and our study of monadic second order equivalence classes.
The respective results are of interest by themselves.
