The rheology of hard-sphere suspensions in the absence of hydrodynamic interactions is examined by Brownian Dynamics. Simulations are performed over a wide range of volume fraction phi and Peclet number Pe = (gamma) over dota(2)/D, where (gamma) over dot is the shear rate and D = kT/6 pi eta a is the Stokes-Einstein diffusivity of an isolated spherical particle of radius a and thermal energy kT in a fluid of viscosity eta. At low Pe, the viscosity decreases as Pe increases-the suspension shear thins. The first normal stress difference is positive, while the second normal stress difference is negative. Each normal stress difference vanishes at very low Pe and increases in magnitude to an extremum at Pe approximate to 3. The suspension pressure is proportional to kT and is found to grow as Pe(2) from its equilibrium value. Long-time self-diffusivities scale as D and grow as Pe is increased in this regime. At Pe approximate to 100, the suspension undergoes a disorder-order transition to a microstructure of hexagonally packed strings aligned in the flow direction, which is accompanied by precipitous drops in the viscosity, pressure and long-time self diffusivities. At high Pe, all components of the stress tensor scale as eta(gamma) over dot and the diffusivities scale as (gamma) over dota(2). Viscosity data for a wide range of phi and Pe are collapsed using scaling theories. (C) 2000 The Society of Rheology. [S0148-6055(00)00403-X].