[en] The two-dimensional conformal field theory has Virasoro algebra as the underlying symmetry. This algebra can be used to describe the coupling of two-dimensional gravity to matter and can be generalized at w-infinity algebra to describe w-gravity. In this paper the gauging of the Virasoro and w-infinity algebras is discussed from the point of view of BRST symmetry. Both algebras are realized as 'Russian formulas' for the curvatures built from the generators of the Lie algebra and the corresponding gauge fields and ghosts. The generalized curvatures are used to determine the gauge invariant Lagrangians as well as the anomaly structures of the conformal two-dimensional theory and the w-gravity. (Author)