  In a series of recent papers we have shown how the dynamical behavior of
certain classical systems can be analyzed using operators evolving according to
Heisenberg-like equations of motions. In particular, we have shown that raising
and lowering operators play a relevant role in this analysis. The technical
problem of our approach stands in the difficulty of solving the equations of
motion, which are, first of all, {\em operator-valued} and, secondly, quite
often nonlinear. In this paper we construct a general procedure which
significantly simplifies the treatment for those systems which can be described
in terms of fermionic operators. The proposed procedure allows to get an
analytic solution, both for quadratic and for more general hamiltonians.
