  We consider gaugeon formulations which discuss the quantum gauge freedom
covariantly in the framework of generalized BRST transformation for the
Yang-Mills theory as well as the BRST invariant Higgs model. We generalize the
BRST symmetries of both the Yang-Mills theory and the Higgs model by making the
transformation parameter finite and field-dependent. Remarkably, we observe
that the gaugeon Lagrangian which describe the quantum gauge freedom appear
automatically in the effective theories along with the natural shift in gauge
parameters under specific finite field-dependent parameters.
