A class of integrable two-dimensional (2D) classical systems with integrals
of motion of fourth order in momenta is obtained from the quantum analogue
s with the help of deformed SUSY algebra. With similar technique a new clas
s of potentials connected with the Lax method is found which provides the i
ntegrability of corresponding 2D Hamiltonian systems. In addition, some int
egrable 2D systems with potentials expressed in elliptic functions are expl
ored.