Liquid-liquid (LL) critical demixing loci have been experimentally determined in the (T,P) projection for some polystyrene/solvent systems with nonspecific interaction for (similar to 270 K < T < similar to 500 K) and (0 MPa < P < 200 MPa). A lower homogeneous double critical pressure and lower homogeneous double critical temperature have been located for a solution of PS (M-w = 2.0 x 10(6)) dissolved in an n-heptane/methylcyclohexane mixture [PS/n-C7H16/CH3C6H11//0.029/0.194/0.777 (wt. fractions)]. That solution forms the first example of a polymer/solvent with nonspecific interaction that exhibits two double critical points. A symmetrical representation of the LL critical loci in the (P,T) plane is developed.