New integrable systems generated by a deformed supersymmetric algebra

New solutions of the intertwining relations for scalar quantum hamiltonians by the second order supercharges with the Lorentz and degenerate metrics are obtained. The symmetry operators for the components of the superhamiltonian are found which result in the integrability of the corresponding quantum systems. The expressions for the hamiltonians and symmetry operators in the classical limit are given. A new class of integrable classical two-dimensional systems possesing the integrals of motion which are of the fourth order in momenta.