  We investigate the Crewther relation at high loop order in a variety of
renormalization schemes and gauges. By examining the properties of the relation
in schemes other than modified minimal subtraction (MSbar) at the fixed points
of Quantum Chromodynamics we propose a generalization of the Crewther relation
that extends the MSbar construction of Broadhurst and Kataev. A derivation
based on the properties of the renormalization group equation is provided for
the generalization which is tested in various scenarios.
