Lattice-Boltzmann simulations of low-Reynolds-number fluid flow in bidisperse fixed beds and suspensions with particle-particle relative motions have been performed. The particles are spherical and are intimately mixed. The total volume fraction of the suspension was varied between 0.1 and 0.4, the volume fraction ratio phi(1)/phi(2) from 1:1 to 1:6, and the particle size ratio d(1)/d(2) from 1:1.5 to 1:4. A drag law with improved accuracy has been established for bidisperse fixed beds. For suspensions with particle-particle relative motions, the hydrodynamic particle-particle drag representing the momentum transfer between particle species through hydrodynamic interaction if found to be an important contribution to the net fluid-particle drag. It has a logarithmic dependence on the lubrication cutoff distance and can be fit as the harmonic mean of the drag forces in bidisperse fixed beds. The proposed drag laws for bidisperse fixed beds and suspensions are generalized to polydisperse suspensions with three or more particle species. (C) 2009 American Institute of Chemical Engineers AIChE J, 55: 1352-13687 2009