  We consider theories characterized by a set of Ward operators which do not
form a closed algebra. We impose the Slavnov--Taylor identity built out of the
Ward operators and we derive the acceptable breaking of the algebra and the
general form of the classical action. The 1PI generating functional is
expressed in terms of the known quantities characterizing the theory and of a
nontrivial integrability condition. As a nontrivial application of our
formalism, we discuss the N=4 supersymmetric nonlinear sigma model.
