Infinite circular corrugated waveguide is analysed to investigate its ability to support modes with backward wave behaviour. Such waveguides provide an alternative structure, easier to manufacture than those already reported based on rectangular symmetry with corrugated walls or filled with frequency selective surfaces. The corrugations if sufficiently deep provide a guiding structure with the required series capacitance and shunt inductance to allow left-handed propagation within some frequency bands. These backward waves are analysed using the surface impedance model of propagation in corrugated waveguides to predict their properties. Interpreting the physical meaning of the analysis, the authors discuss how backward waves are related to resonances in corrugated structures. The relationship between power flows in the guide and the behaviour of the group velocity for such guides is shown. A full wave simulator is also applied to validate these results and the case of a dielectric filled waveguide is considered showing the improved ability to support left-handed modes. The authors present the results of a parametric study of how left-handed propagation depends on the corrugation depth. Potential applications of backward waves in corrugated circular waveguides are proposed.