The phase behaviour of blends of poly(methyl methacrylate) (PMMA) and poly(styrene-co-acrylonitrile) (SAN) is calculated as a function of copolymer composition from the data of the temperature dependence of all three segmental interaction parameters, chi(i/j)(T) of the system SAN/PMMA, i.e. chi(S/MMA)(T), chi(AN/MMA)(T) and chi(S/AN)(T). Using blends with different copolymer compositions might change the temperature dependence of the polymer-polymer interaction parameter chi(AB)(T) dramatically, from increasing to decreasing with temperature. In the copolymer composition range from similar to 11 to 55 mol% of acrylonitrile in SAN the chi(AB)(T) parameter is increasing with temperature, leading to lower critical solution temperature behaviour, and in the copolymer composition range up to similar to 10 mol% and > 56 mol% of AN in SAN the chi(AB)(T) parameter is decreasing with increasing temperature, predicting upper critical solution temperature behaviour when one or two components have relatively low molecular weight, i.e. for oligomers. Similar conclusions can be obtained for blends of SAN with poly (epsilon-caprolactone).