  We find a new type of non-linear supersymmetries, called N-fold
parasupersymmetry, which is a generalization of both N-fold supersymmetry and
parasupersymmetry. We provide a general formulation of this new symmetry and
then construct a second-order N-fold parasupersymmetric quantum system where
all the components of N-fold parasupercharges are given by type A N-fold
supercharges. We show that this system exactly reduces to the
Rubakov-Spiridonov model when N=1 and admits a generalized type C 2N-fold
superalgebra. We conjecture the existence of other `N-fold generalizations'
such as N-fold fractional supersymmetry, N-fold orthosupersymmetry, and so on.
