  We derive two new classes of integrable theories interpolating between exact
CFT WZW or gauged WZW models and non-Abelian T-duals of principal chiral models
or geometric coset models. They are naturally constructed by gauging symmetries
of integrable models. Our analysis implies that non-Abelian T-duality preserves
integrability and suggests a novel way to understand the global properties of
the corresponding backgrounds.
