  We discuss a spectrum generating algebra in the supersymmetric quantum
mechanical system which is defined as a series of solutions to a specific
differential equation. All Hamiltonians have equally spaced eigenvalues, and we
realize both positive and negative mode generators of a subalgebra of
$W_{1+\infty}$ without use of negative power of raising/lowering operators of
the system. All features in the supersymmetric case are generalized to the
parasupersymmetric systems of order 2.
