The rheological properties of dense suspensions of bimodal mixtures of colloidal particles with long-range, soft repulsions were investigated. Suspensions of particles suspended in 10(-4) M KCI with volume fractions ranging from 0.3-0.6 were studied for volume fraction ratios of large to small particles of 0, 0.25, 0.5, 0.75, and 1.0. Latex particles of diameters ranging between 105 to 544 nm were used. These particles were stabilized by a combination of electrostatic and short range steric repulsions. Four separate mixtures were investigated with size ratios (large/small) of 1.2-5. At volume fractions investigated, the suspensions displayed dynamic yield stresses, tau(y), and shear thinned with increasing stress or shear rate. The yield stress was found to be proportional to the suspension's elastic modulus, with a constant of proportionality lying between 0.015 and 0.03 as has been reported for a wide range of monodisperse suspensions. The functional dependence of stress on shear rate could be reduced to a single master curve which was independent of volume fraction, particle size ratio, and mixing ratio by scaling tau(y) on G, and the shear rate on G/eta(c) where eta(c) is the continuous phase viscosity. In bimodal suspensions sheat thickening accompanied by irreversible aggregation was observed at volume fractions substantially below that measured for monodisperse suspensions. The stress and sheat rate at thickening decreased rapidly as the volume fraction of the mixed suspension was increased. These results are substantially different than what has been reported for well-mixed suspensions of particles experiencing "hard" repulsions in that as the fraction of large particles is increased no viscosity minimum is seen at low and intermediate shear rates.