Liquid-crystal polymers often exhibit a low-shear-rate region of shear thinning of viscosity, accompanied by lack of net orientation and by a dependence of texture and rheology on shear history. A phenomenological model to account for this region is presented. The model uses Marrucci's description of stable domains whose size is a function of stress. The interaction of these domains is estimated from the continuum theory of liquid crystals. The shear-rate-dependent viscosity and normal stress of the polydomain fluid are calculated from the interaction energy and size of the domain by analogy with non-equilibrium molecular-dynamics calculations for small-molecule fluids. The shear-rate dependences are similar to those observed experimentally. Other tests of the model, including optical observations and measurement of dynamic viscosity, are proposed.