In hard-sphere suspensions of solid particles, the stress has the Brownian (thermodynamic) and hydrodynamic components σB and σH, the former reflecting the anisotropy of the particle distribution while the latter being determined by the hydrodynamic interaction between the particles. These two components exhibit nonlinearities under steady shear flow with different mechanisms. The nonlinearity of σB results from the particle distribution insensitive to the shear rate, while σH becomes nonlinear due to flowinduced clustering of the particles. These structural origins of the nonlinearities were confirmed from flow-SANS experiments