Real submanifolds in complex spaces

Let (z 11,..., z 1N ,..., z m1,..., z mN , w 11,..., w mm ) be the coordinates in CmN+m2. In this note we prove the analogue of the Theorem of Moser in the case of the real-analytic submanifold M defined as follows W=ZZ....t+O(3), where W = {w ij }1.i,j.m and Z = {z ij }1.i.m, 1.j.N . We prove that M is biholomorphically equivalent to the model W=ZZ....t if and only if is formally equivalent to it.