A free-diffusion method has been developed for the determination of the intradiffusion coefficient ('self-diffusion coefficient') of a polymer in highly concentrated solutions. A fraction of the polymer is labelled with a small amount of light-absorbing substituent. The diffusion of this labelled species, present in low concentration, is followed in the presence of a high concentration of unlabelled material with the aid of absorption optics in the analytical ultracentrifuge. The diffusion proceeds over a boundary at which the difference in concentration of unlabelled material is varied. The average concentration of total polymer and the concentration of the labelled material are, however, constant. From theoretical considerations it is shown that by extrapolation of the diffusion coefficient so obtained to zero concentration difference of total material, the intradiffusion coefficient of the polymer at that concentration is obtained. The procedure also permits the ordinary translational diffusion coefficient to be estimated. The method has been applied to two dextran fractions with weight-average molecular weights of 19000 and 150000, which were labelled with fluorescein groups. As expected, the intradiffusion coefficient decreases with increasing polymer concentration, the decrease being more pronounced for the high-molecular-weight material. This decrease in the diffusion rate of dextran is, however, less than the corresponding decrease in the sedimentation rate which proteins with similar hydrodynamic parameters experience in dextran solutions. This agrees with the hypothesis that flexible linear polymers move through a network as chains rather than as hydrodynamic spheres. By combining measurements of the ordinary diffusion coefficient and the intradiffusion coefficient, it is possible to calculate the thermodynamic properties (as expressed by the virial expansion) of the system. This method is of particular importance in studies on concentrated solutions of high-molecular-weight polymers.