The translational diffusion constants, D, of biphenyl, diphenylacetylene, diphenylbutadiyne, anthracene, pyrene, rubrene, perylene, and coronene have been determined in the n-alkanes using capillary flow techniques. Pyrene and rubrene were also studied in cyclohexane and several of its derivatives. The solutes showed varying degrees of deviation from the Stokes-Einstein (SE) relation (D = k(B)T/6 pi etar); the values of the hydrodynamic radius r decrease as the viscosity eta increases. The data can be fitted to D/T = A/eta (p) with p < 1 (p = 1 for the SE relation). The values of p increase as the solute size increases. In the n-alkanes, they range from p = 0.718 +/- 0.004 for biphenyl to p = 0.943 +/-0.014 for rubrene; the largest value (p = 0.982 +/- 0.019) is found for rubrene in the cyclohexanes. The D values have been compared with reorientational results and molecular dynamics calculations; they have also been fitted to the Doolittle-Cohen-Turnbull free volume equation. A correlation between the p values and the results of the free volume analyses is discussed.