  The rules of local superfield Lagrangian quantization in reducible
non-Abelian hypergauge functions are formulated for an arbitrary gauge theory.
The generating functionals of standard and vertex Green's functions which
depend on the Grassmann variable $\eta$ via super(anti)fields and sources are
constructed. The difference between the local quantum and the gauge fixing
actions determines an almost Hamiltonian system such that translations with
respect to $\eta$ along the solutions of this system define the superfield BRST
transformations. The Ward identities are derived and the gauge independence of
the S-matrix is proved.
