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The phenomenon of co-nonsolvency, i.e. the formation of nonsolvents by mixing two solvents, was studied for the system N,N-dimethylformamide/cyclohexane/polystyrene (DMF/CH/PS) which is characterized by the fact that the components of the mixed solvent are only incompletely miscible below 48,6°C. A number of quasibinary sections (stepwise addition of the second solvent to given solutions of the polymer in the first solvent) for a sample (M = 110000) of high molecular uniformity yielded a cloud point surface which gives “island curves” (closed solubility gaps) for constant temperatures between the critical temperature of DMF/CH and the top of the cloud point surface (51,3°C). The attainment of equilibrium is facilitated by the addition of DMF to CH or solutions of PS in CH, as compared with the opposite procedure. By means of phase equilibrium experiments tie lines and the critical curve could also be constructed. For a theoretical calculation of the latter from information concerning the binary sub-systems (e.g. light scattering of PS in DMF) the single liquid approximation was applied to DMF/PS instead of—with respect to miscibility—the more dissimilar DMF/CH; the results are in qualitative accord with experimental observations. Orienting measurements concering the chain length dependence of the partition coefficient in co-nonsolvent systems indicate that their aptitude for fractionation is considerably worse than that of normal systems under comparable conditions.