  We investigate 't Hooft's technique of changing the gauge parameter of the
linear covariant gauge from the point of view of the path integral with respect
to the gauge freedom. Extension of the degrees of freedom allows us to
formulate a system with extended gauge symmetry. The gauge fixing for this
extended symmetry yields the 't Hooft averaging as a path integral over the
additional degrees of freedom. Another gauge fixing is found as a non-abelian
analogue of the type II gaugeon formalism of Yokoyama and Kubo. In this
connection, the 't Hooft average can be viewed as the analogue of the type I
gaugeon formalism. As a result, we obtain gauge covariant formulations of
non-abelian gauge theories, which allow us to understand 't Hoot's technique
also from the canonical fromalism.
