  We find the conditions under which a Riemannian manifold equipped with a
closed three-form and a vector field define an on--shell N=(2,2) supersymmetric
gauged sigma model. The conditions are that the manifold admits a twisted
generalized Kaehler structure, that the vector field preserves this structure,
and that a so--called generalized moment map exists for it. By a theorem in
generalized complex geometry, these conditions imply that the quotient is again
a twisted generalized Kaehler manifold; this is in perfect agreement with
expectations from the renormalization group flow. This method can produce new
N=(2,2) models with NS flux, extending the usual Kaehler quotient construction
based on Kaehler gauged sigma models.
