in this talk we investigate what kind of cr manifolds have the following local uniqueness property: if two holomorphic functions have the same modulus on the manifold they are equal (up to a constant) in the whole space. minimal generic submanifolds have this property. we will investigate the nonminimal case and we will give a sufficient geometric property which we will call almost minimality. this condition is related to the manifold being contained in a possibly singular real analytic levi-flat hypersurface.