The shear-induced phase transitions of binary polymer mixtures have been studied. We solved the two-fluid model numerically in a high Weissenberg number and infinite Peclet number flow regime without linearization of the diffusive equation or the adiabatic approximation. Our simulations have captured key features of flow-induced phase transitions, such as the shift in the phase boundary from the equilibrium phase diagram under flow conditions. Both shear-induced mixing and demixing phenomena have been reproduced. The dynamic phase behavior of polymer mixtures is governed by parameters including phi(A) and chi for thermodynamic forces, tau(') and G(') for the degree of dynamical asymmetry in polymer mixtures, and the imposed nominal shear rate. Dynamic phase diagrams are obtained for steady state flow. We have identified correlations between the microstructure evolution and rheology, and a mechanism to reach the steady state. The rheological signature of demixing fluids under shear is that the dependence of the steady state shear stress on shear rate changes from nonlinear to linear within that range of shear rates in which the demixing occurs. (C) 2003 American Institute of Physics.