  We determine the equations which govern the gauge symmetries of worldsheets
with local supersymmetry of arbitrary rank $(N,N')$, and their possible
anomalies. Both classical and ghost conformally invariant multiplets of the
left or right sector are assembled into the components of a single
$O(N)$-superfield. The component with ghost number zero of this superfield is
the $N$-supersymmetric generalization of the Beltrami differential. In a
Lagrangian approach, and after gauge-fixing, it becomes the super-moduli of
Riemann surfaces coupled to local supersymmetry of rank $N$. It is also the
source of all linear superconformal currents derived from ordinary operator
product techniques. The interconnection between BRST invariant actions with
different values of $N\geq 3$, and their possible link to topological
2D-gravity coupled to topological sigma models, are shown by straightforward
algebraic considerations.
