A study has been made of the viscoelastic behaviour of a range of supercooled liquids each of which has a steady-flow viscosity η fitting the equation, ln η=A′+ B′/(T–T0), where T0 is the reference temperature at which no free-volume is available for molecular translational motion. For all the liquids investigated, the limiting shear rigidity modulus G∞ varies with temperature according to the relationship, 1//G∞ =1//G0 +a0//G1 (T–T0), where a0 is the coefficient of thermal expansion and G0 the shear modulus at temperature T0, and G1 is a shear modulus associated with the weakening of the intermolecular force field due to an increase in free-volume with increasing temperature. The complete linear viscoelastic behaviour can be calculated from a knowledge of the dependence upon temperature of the density, steady-flow viscosity and limiting shear rigidity modulus. Details are given of the new liquid model on which these predictions are based, together with ample experimental confirmation.