Quartz crystals resonant in the fundamental torsional mode at frequencies of 40 and 73 kc/s have been used to measure the viscoelastic properties of solutions of polystyrene in toluene, methyl ethyl ketone and cyclohexane. A monodisperse polystyrene sample of molecular weight 2.39 x 10$^5$ was employed. The results have been compared with those of Harrison, Lamb & Matheson (1964) for dilute solutions in toluene of a number of polystyrene samples of different molecular weights. In toluene it is found that 25% of the contribution of the polymer to the viscosity of the solution is not able to take part in viscoelastic relaxation, and that the dynamic viscosity at high frequencies (the 'Einstein viscosity') is greater than the solvent viscosity. Under these conditions the viscoelastic behaviour of all the solutions in toluene of polystyrene samples of different molecular weights agrees with the predictions of the Rouse theory. From the value obtained for the Einstein viscosity of the solutions, it is shown that the radius of the equivalent hydrodynamic sphere is approximately proportional to the square root of the molecular weight of the polymer molecule. If one assumes that the radius of the equivalent hydrodynamic sphere of a given polymer molecule is the same in all solvents, then the viscoelastic behaviour of the solution in methyl ethyl ketone is intermediate between the predictions of the Zimm and Rouse theories. The solution in cyclohexane seems to show behaviour close to that predicted by the Zimm theory. The possibility of using such measurements to determine molecular weight distributions is discussed.