  We consider target space duality transformations for heterotic sigma models
and strings away from renormalization group fixed points. By imposing certain
consistency requirements between the T-duality symmetry and renormalization
group flows, the one loop gauge beta function is uniquely determined, without
any diagram calculations. Classical T-duality symmetry is a valid quantum
symmetry of the heterotic sigma model, severely constraining its
renormalization flows at this one loop order. The issue of heterotic anomalies
and their cancelation is addressed from this duality constraining viewpoint.
