The effects of shear flow on the phase behavior of a polymer blend with high glass transition temperature (T-g) constituents possessing a large viscosity difference were investigated using shear and capillary rheometry, complemented by differential scanning calorimetry and analysis of the extrudates with scanning electron microscopy. The blend is a lower critical solution temperature polymer mixture of a random copolymer of styrene and maleic anhydride, SMA (T-g = 178 degrees C), and poly(methyl methacrylate), PMMA, (T-g = 105 degrees C). Depending on temperature, both shear-induced mixing, typically, at very high shear rates, and shear-induced demixing, typically, at moderate shear rates, were observed. In the former case, extrudates were optically transparent, yielding one T-g and were thermorheologically simple at all temperatures below and up to the capillary extrusion one. On the other hand, extrudates related to shear-induced demixing were opaque, yielding two distinct T-g＇s and were thermorheologically complex. The experimental methodology presented here for the determination of the shear-phase diagram in a flowing polymer blend should be applicable to any industrial mixture, and it is of particular value for assessing the effects of strong shear flow, relevant in polymer processing applications. Finally, the method of blend preparation, i.e., solution-cast versus melt-mixed samples, affected slightly the rheologically determined demixing temperatures.