A two-dimensional model of flow and bed topography is proposed to investigate the effect of sediment heterogeneity on the development of alternate bars. Within the context of a linear stability theory the flow field, the bed topography and the grain size distribution function are perturbed leading to an integro-differential linear eigenvalue problem. It is shown that the selective transport of different grain size fractions and the resulting spatial pattern of sorting may appreciably affect the balance between stabilizing and destabilizing actions which govern bar instability. Theoretical results suggest that sediment heterogeneity leads to a damping of both growth rate and migration speed of bars, while bar wavelength is shortened with respect to the case of uniform sediment. The above findings conform, at least qualitatively, to the experimentally detected reduction of bar height, length and celerity. The observed tendency of coarser particles to pile up towards bar crests is also reproduced by theoretical results.