Let M-n subset of Rn+2, n greater than or equal to 7, be a conformally defo
rmable submanifold of euclidean space in codimension two. In this paper we
show that if the submanifold has sufficiently low conformal nullity, a gene
ric conformal condition, then it can be realized as a hypersurface of a con
formally deformable hypersurface. The latter have been classified by Cartan
early this century. Furthermore, it turns out that all deformations of the
former are induced by deformations of the latter.