  In this work limit probabilities of first-order properties of the random
$s$-uniform hypergraph in the binomial model $G^{s}(n,p)$ are studied. We give
a complete discription of all positive $\alpha$ such that
$G^{s}(n,n^{-\alpha})$ obeys Zero-One Law. Moreover, for any rational $\rho\geq
1/(s-1)$ we prove the existence of a strictly balanced $s$-uniform hypergraph
with the density $\rho$.
