The elastic-like and viscous-like viscosity components of model, Brownian hard sphere suspensions were determined. The elastic-like component, sometimes called the thermodynamic component, is due to Brownian motion while the viscous-like component, sometimes called the hydrodynamic component, is due to hydrodynamic interaction between and drag on the particles. The three volume fractions tested were found to be above the glass transition volume fraction due to the absence of a zero shear viscosity. The hydrodynamic viscosity component was approximately independent of shear rate, yet the suspension demonstrated a large amount of shear thinning which was due to the elastic like component. The measured stress components associated with shear thickening were distinctly different in each sample. Continuous shear thickening was measured for the sample with 0.54 volume fraction while the samples with volume fractions 0.59 and 0.63 showed discontinuous shear thickening. Shear thickening in these concentrated suspensions was related to the effect of particle clustering increasing the effective volume fraction above maximum packing fraction. The type of shear thickening changed from being viscous-like for the two lower volume fractions, indicating the formation of particle clusters, to elastic-like for the highest volume fraction. Stress decay after cessation of shear was found to follow a power law relation with time indicative of fractal-like microstructures.