We have performed a series of molecular dynamics simulations of water-dimethyl sulfoxide (DMSO) mixtures containing either an ionic or a neutral atomic solute to investigate the effects of composition of the mixture on the diffusion of these solutes. Several different compositions of the mixtures ranging from pure DMSO to pure water are considered. Altogether, 23 different systems are simulated in the present work. The diffusion coefficients of both ionic and neutral solutes are found to show strong nonideal behavior with variation of composition of the solvent mixture. The extent of nonideality of the solute diffusion is found to be similar to the nonideality that is observed for the diffusion and orientational relaxation of water and DMSO molecules in these mixtures and is attributed to the presence of rather strong water-DMSO hydrogen bonds in these mixtures. The simulation results are compared with those of experiments wherever available. (C) 2003 American Institute of Physics.