The main features of the critical line in presure-temperature-composition space for mixtures containing either a linear or a cyclic poly(dimethylsiloxane) (PDMS) in tetramethylsilane (TMS) are predicted through the use of the Patterson modification of Prigogine’s corresponding-states theory, which incorporates the cell model of a liquid together with a simple van der Waals dependence of the configurational energy on volume. Two main kinds of critical lines are obtained : one is a continuous line for those mixtures with a small chain-length difference between the components, leading to a fairly good prediction of the liquid vapour critical temperatures of the pure substances; and the other is a broken line for mixtures with a large chain-length difference between the polymer and solvent, indicating the occurrence of a lower critical threshold temperature (LCTT) at low polymer concentrations. A full set of temperature and pressure reduction parameters for both linear and cyclic oligomers and PDMS are reported, and are used as the basis for all the calculations with no adjustment whatsoever. It is predicted that the system of minimum chain length to show an LCTT is that containing a PDMS of 24 skeletal bonds, compared to the methane-hexane system in the n-alkanes, thus giving an insight into the more flexible and more expanded nature of the PDMS series. Results for the interaction parametert chi1 confirm that any difference in chemical nature between TMS and the PDMS series may be largely ignored since the structural term c1tau alone can account for the LCTT behaviour.