  Parasupersymmetric quantum mechanics is exploited to introduce a topological
invariant associated with a pair of parameter dependent Fredholm (respectively
elliptic differential) operators satisfying two compatibility conditions. An
explicit algebraic expression for this topological invariant is provided. The
latter identifies the parasupersymmetric topological invariant with the sum of
the analytic (Atiyah-Singer) indices of the corresponding operators.
