  This paper presents a careful derivation of the quasiclassical equations of
superconductivity so that a manifest gauge invariance is retained with respect
to the space-time arguments of the quasiclassical Green's function $\hat{g}$.
The terms responsible for the Hall effect naturally appear from the derivation.
The equations are applicable to clean as well as dirty superconductors for an
arbitrary external frequency much smaller than the Fermi energy. Thus, they
will form a basis toward a complete microscopic understanding of the Hall
effect in type-II superconductors.
