In this paper, certain anomalous effects are investigated which appear when results recorded on the eccentric-cylinder and displaced-hemisphere rheometers are compared (cf parts I and II) with results obtained from oscillatory tests on a Weissenberg rheogoniometer. These irregularities are prominent in highly viscous, nearly Newtonian, and elastico-viscous liquids, and it will be shown how they occur in direct contrast to results taken for more mobile systems. Interpretation of experimental results for highly viscous fluids from the rheometers suggests that the fluids are less viscous and more elastic than would be indicated by the rheogoniometer results.For a given material these irregular effects increase with rotational speed, while for a constant rotational speed, they increase for increasingly viscous fluids. The zero-shear viscosity in the case of the elastico-viscous systems does not appear to be a significant factor; it is rather the dynamic viscosity appropriate to the operating frequency which determines the extent of the irregular effects.Various possible causes of the anomalous effects are systematically eliminated, and it is ultimately concluded that they are due to `cavitation' effects in the new rheometers.