“…In this letter, we report on a new type of non-linear supersymmetries, called N -fold parasupersymmetry, which is a generalization of both N -fold supersymmetry [1, 2,3] and parasupersymmetry [4,5,6,7,8]. In our previous paper [9], we generically formulated parasupersymmetry and showed that parasupersymmetric quantum systems as well as N -fold supersymmetric ones are weakly quasi-solvable. The latter fact implies that corresponding higher-dimensional quantum field theories, if exist, would satisfy some kinds of perturbative non-renormalization theorems, as in the case of ordinary supersymmetric quantum field theory, since quasi-solvability is a one-dimensional analog and, in a sense, a generalization of the theorems [2].…”