The translational diffusion constants, D, of trans-stilbene, 1,4-dipheny-1,3-butadiene, 1,6-dipheny-1,3,5-hexatriene, 1,1,4,4,-tetraphenyl-1,3-butadiene, tetraphenylethylene, 9,10-diphenylanthracene,p-terphenyl, bibenzyl, 1,1'-binaphthyl, [2.2]paracyclophane, triptycene, and dodecahydrotriphenylene have been determined in the n-alkanes using capillary flow techniques. The solutes showed deviations from the Stokes-Einstein (SE) relation (D = k(B)T/(6pietar)); the values of the hydrodynamic radius, r, decrease as the viscosity, eta, increases. The data can be fitted to D/T = A(SE)/eta(p) with p < 1 (p = 1 for the SE relation). The values of p increase as the solute size increases; they range from p = 0.712 for p-terphenyl to p = 0.942 for 1,1,4,4,-tetraphenyl-1,3-butadiene. The deviations from SE behavior are discussed in terms of the ratio V-s/V-p, where V-s and V-p are the van der Waals volumes of a solvent and diffusing probe, respectively. The diffusion constants also are discussed in terms of the Wilke-Chang equation. The values of D-1 for several of the solutes are compared with their rotational correlation times, re, in the n-alkanes. The values of re, which showed deviations from the Stokes-Einstein-Debye expression (tau(theta) = 4pir(3)eta/(3k(B)T)), have the same general dependence on viscosity as D-1.