A recently developed (Ponte Castañeda 2002 J. Mech. Phys. Solids 50, 737–757) ‘second–order’ nonlinear homogenization method is used to estimate the constitutive response of reinforced and other Bingham composites. For the special case of rigidly reinforced Bingham composites with overall isotropy (in two dimensions), the results show that the homogenized response of such materials is not strictly Bingham. Thus, instead of a purely linear incremental response beyond the relevant threshold (yield) stress, the response is strongly nonlinear just after yield and asymptotes to a purely linear incremental response only at sufficiently large stress or strain–rate levels. This phenomenon is linked to the presence of strong fluctuations of the strain–rate field in the composite at the onset of yield.