The N = 2 superdiffeomorphism anomaly is defined on the compact N = 2 super
-Riemann surfaces by the inclusion of N = 2 superprojective connection. The
N = 2 supercovariant operators which are superconformally covariant are co
nstructed and the relations with the N = 2 super-Poisson operators and the
Krichever-Novikov algebra are given. (C) 2000 American Institute of Physics
. [S0022-2488(00)00401-1].