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We extensively investigate two-step shape invariance in the framework ofN-fold supersymmetry. We first show that any two-step shape-invariant systempossesses type A 2-fold supersymmetry with an intermediate Hamiltonian and thushas second-order parasupersymmetry as well. Employing the general form of typeA 2-fold supersymmetry, we systematically construct two-step shape-invariantpotentials. In addition to the well-known ordinary shape-invariant potentials,we obtain several new and novel two-step shape-invariant ones which are notordinary shape invariant. Furthermore, some of the latter potentials areconditionally two-step shape invariant and thus are conditionally solvable.

Two-step Shape Invariance in the Framework of N-fold Supersymmetry