  We report general forms of one family of the N-fold supersymmetry in
one-dimensional quantum mechanics. The N-fold supersymmetry is characterized by
the supercharges which are N-th order in differential operators. The family
reported here is defined as a particular form of the supercharges and is
referred to as ``type A''. We show that a quartic and a periodic potentials,
which were previously found to be N-fold supersymmetric by the authors, are
realized as special cases of this type A family.
