An H-system \(<\alpha;a>\) over a group (A,.) is said to be: 1) an \(E_ n\)-system if \(\alpha (x)=x^ m\); 2) a PH-system if a is the neutral element of (A,.). In this paper the author gives conditions for G-systems \(<\beta^ n_ 1;b>\) over (A,.) which ensure that the (n\(+1)\)-group \(der^ n_{\beta;b}(A,.)\) is isomorphic to some \((n+1)\)-group \(E_ m\)- , PH- or \(PE_ m\)-derived from (A,.), respectively.