Authors’ abstract: It is shown that for any real-analytic submanifold \(M\) in \({\mathbb C}^N\) there is a proper real-analytic subvariety \(V \subset M\) such that for any \(p\in M-V\), any real analytic submanifold \(M'\) in \({\mathbb C}^N\), 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 any \(p\in M-V\), the problem of biholomorphic equivalence of the germs of \((M, p)\) 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.