Viscoelastic properties of polystyrene/poly(vinyl methyl ether) blends with nearly critical compositions were measured under steady-shear flows near the phase separation temperatures. In the homogeneous region, shear rate dependences of shear viscosity eta and shear compliance J(S) are practically the same as those of homopolymers. In the phase-separated region at quiescence, on the other hand, eta and J(S) are enhanced at low shear rates, but they become almost the same as those in the homogeneous region when the shear rates are higher than their respective critical shear rates. The critical shear rate values from J(S), gamma(cJ), were found to be larger than those from eta, gamma(cV), and gamma(cJ) is considered to be almost equal to the critical shear rate for shear-induced homogenization gamma(c). Moreover, it was pointed out that, when gamma(cV) is smaller than the critical shear rate for non-Newtonian behavior of eta, there exists a plateau region in the shear rate dependence of eta.