  A convenient formalism is developed to treat classical dynamical systems
involving $(p=2)$ parafermionic and parabosonic dynamical variables. This is
achieved via the introduction of a parabracket which summarizes the
paracommutation relations of the corresponding Green components in a unified
manner. Furthermore, it is shown that Peierls quantization scheme may be
applied to such systems provided that one uses the above mentioned parabracket
to express the quantum paracommutation relations. Application of the Peierls
scheme also provides the form of the parafermionic and parabosonic kinetic
terms in the Lagrangian.
