  Starting from flat two-dimensional gauge potentials we propose the notion of
${\cal W}$-gauge structure in terms of a nilpotent BRS differential algebra.
The decomposition of the underlying Lie algebra with respect to an $SL(2)$
subalgebra is crucial for the discussion conformal covariance, in particular
the appearance of a projective connection. Different $SL(2)$ embeddings lead to
various ${\cal W}$-gauge structures. We present a general soldering procedure
which allows to express zero curvature conditions for the ${\cal W}$-currents
in terms of conformally covariant differential operators acting on the ${\cal
W}$ gauge fields and to obtain, at the same time, the complete nilpotent BRS
differential algebra generated by ${\cal W}$-currents, gauge fields and the
ghost fields corresponding to ${\cal W}$-diffeomorphisms. As illustrations we
treat the cases of $SL(2)$ itself and to the two different $SL(2)$ embeddings
in $SL(3)$, {\it viz.} the ${\cal W}_3^{(1)}$- and ${\cal W}_3^{(2)}$-gauge
structures, in some detail. In these cases we determine algebraically ${\cal
W}$-anomalies as solutions of the consistency conditions and discuss their
Chern-Simons origin.
