  In the paper a set of necessary and sufficient conditions for
\textit{v-}sufficiency (equiv. \textit{sv-}sufficiency) of jets of map-germs
$f:(\mathbb{R}^{n},0)\to (\mathbb{R}^{m},0)$ is proved which generalize both
the Kuiper-Kuo and the Thom conditions in the function case ($m=1$) so as the
Kuo conditions in the general map case ($m>1$). Contrary to the Kuo conditions
the conditions proved in the paper do not require to verify any inequalities in
a so-called horn-neighborhood of the (a'priori unknown) set $f^{-1}(0)$.
Instead, the proposed conditions reduce the problem on \textit{v-}sufficiency
of jets to evaluating the local {\L}ojasiewicz exponents for some
constructively built polynomial functions.
