  We establish a formal variational calculus of supervariables, which is a
combination of the bosonic theory of Gel'fand-Dikii and the fermionic theory in
our earlier work. Certain interesting new algebraic structures are found in
connection with Hamiltonian superoperators in terms of our theory. In
particular, we find connections between Hamiltonian superoperators and
Novikov-Poisson algebras that we introduced in our earlier work in order to
establish a tensor theory of Novikov algebras. Furthermore, we prove that an
odd linear Hamiltonian superoperator in our variational calculus induces a Lie
superalgebra, which is a natural generalization of the Super-Virasoro algebra
under certain conditions.
