This paper re-examines the 'proof' of Cheng and Evans (1965) that the equilibrium flow curve of a thixotropic fluid has a positive slope, and shows that the slope can indeed be negative in parts. The implication of this on thixotropic behaviour in viscometers is described. Such thixotropic fluids can develop shear banding in wide-gap viscometers in common with many other materials, a brief survey of which is given. Additionally, the interrelationship of the Cross and Sisko fluids as models of thixotropy is examined, leading to the creation of a new class of thixotropic models.