We show that for any real-analytic submanifold $M$ in $\Bbb C^N$ there is a proper real-analytic subvariety $V\subset M$ such that for any $p \in M\setminus V$, any real-analytic submanifold $M'$ in $\Bbb C^N$, and any $p' \in M'$, the germs $(M,p)$ and $(M',p')$ of the submanifolds $M$ and $M'$ at $p$ and $p'$ respectively are formally equivalent if and only if they are biholomorphically equivalent. As an application, for $p\in M\setminus V$, the problem of biholomorphic equivalence of the germs $(M,p)$ and $(M',p')$ is reduced to that of solving a system of polynomial equations. More general results for $k$-equivalences are also stated and proved.