The thermodynamic interactions in the ternary mixture tetrahydrofuran/gamma-butyrolactone/poly(ether imide) (THF/ gamma-BL/PEI) are investigated from 30 to 50 degrees C. This is a membrane-forming system with a high He-selectivity. Cloud point measurements show that the two binary polymer solutions THF/PEI and gamma-BL/PET exhibit miscibility gaps which close towards the centre of the ternary phase diagram where the mixtures become homogeneous (cosolvency). Vapour pressures were determined for the subsystem THF/gamma-BL. For the theoretical calculations the Gibbs energy of mixing is formulated according to the Flory-Huggins theory and the interaction parameter chi(THF/gamma-BL) calculated from the vapour pressures. The adjustment of theoretical phase diagrams to the experimental data (cloud point curves, tie lines and critical points) gives access to chi(THF/PEI) and chi(gamma-BL/PEI) For a satisfactory representation of the liquid-liquid demixing, a concentration dependent chi(THF/PEI) is required, whereas concentration independent values for chi(THF gamma-BL) and chi(gamma-BL/PEI) suffice.