As a preparation for the study of arbitrary extensions of d = 2 gravity we present a detailed investigation of SO(N ) supergravity. Induced d = 2, SO(N ) supergravity is constructed by gauging a chiral, nilpotent subgroup of the OSp(N |2) Wess-Zumino-Witten model. In order to get a gauge invariant theory with the correct number of degrees of freedom, we need to introduce N free fermions. From this we derive an all order expression for the effective action. Reality of the coupling constant imposes the usual restrictions on c for N = 0 and 1. No such restrictions appear for N ≥ 2. For N = 2, 3 and 4, no renormalizations of the coupling constant beyond one loop occur. Also, the effective N = 4 gravity based upon a linear N = 4 superconformal algebra, there is no renormalization at all, i.e. the quantum theory is equal to the classical. These results are related to non-renormalization theorems for theories with extended supersymmetries. Arbitrary (super)extensions of d = 2 gravity are then analyzed. The induced theory is represented by a WZW model for which a chiral, solvable group is gauged. From this, we obtain the effective action. All order expressions for both the coupling constant renormalization and the wavefunction renormalization are given. From this we classify all extensions of d = 2 gravity for which the coupling constant gets at most a one loop renormalization. As an application of the general strategy, N = 4 theories based on D(2, 1, α) and SU (1, 1|2), all W A gravities and the N = 2 W n models are treated in some detail. * This work was supported in part by the