The behaviour of nearly neutrally-buoyant suspensions has been studied experimentally, using a concentric-cylinder rheometer. The effect on the suspension viscosity of: (i) solid fraction, (ii) diameter of the solid, spherical particles, (iii) viscosity of the suspending liquid, and (iv) shear rate has been determined experimentally, where all suspensions have been created using the same particulate and liquid materials. The suspension behaviour can well be described by the Ostwald-de Waele model, i.e. a power-law relation between shear stress and shear rate. For low solid fractions, the behaviour is nearly Newtonian, while for larger solid fractions shear thinning behaviour is observed. The relative viscosity, i.e. the ratio between suspension and liquid viscosities, is a rapidly increasing function of solid fraction. For suspensions based on a liquid with high viscosity, the effect of the particle diameter is small, while for those with a low liquid viscosity, the suspension viscosity decreases weakly with increasing particle diameter. The relative viscosity is higher for systems based on a liquid with low viscosity, in comparison with systems with a high liquid viscosity. The current investigation shows that commonly used relations for the relative viscosity of suspensions, that only include solid fraction and a maximum solid fraction, are not generally valid.