  Anomalies of N = (4,4) superconformal field theories coupled to a conformal
supergravity background in two dimensions are computed by using the AdS/CFT
correspondence. We find that Weyl, axial gauge and super Weyl transformations
are anomalous, while general coordinate, local Lorentz, vector gauge and local
super transformations are not. The coefficients of the anomalies show that the
superconformal field theories have the central charge expected in the AdS/CFT
correspondence.
