Within a BRST formulation, we determine the expressions of the consist
ent anomaly for superstrings with extended worldsheet supersymmetries
of rank N. We consider the O(N) superconformal algebras up to N = 4, a
s well as the 'small N = 4' superalgebra. This is done using a superfi
eld formalism, allowing to recover previous results that were expresse
d in components. Moreover, we identify the 'small N = 4' algebra as th
e constrained 'large N = 4' via a self-duality like condition in super
space. (C) 1997 Elsevier Science B.V.