The self-diffusion coefficients of the three components of a salt-free heavy-water solution of polymethacrylic acid, completely neutralized with tetra-methylammonium hydroxide, were measured over a broad concentration range. Three concentration regions were observed for the self-diffusion of both the polyions and the counterions. At polyion concentrations below 0.01 mol monomer kg^-1, the dilute concentration regime for the polymer, the polyion self-diffusion coefficient approaches the self-diffusion coefficient of a freely diffusing rod upon dilution. At polyelectrolyte concentrations above 0.1 mol monomer kg^-1, the self-diffusion coefficients of the solvent, the counterions and the polymer decreased with concentration, suggesting that this decrease is due to a topological constraint on the motions of the components. In the intermediate-concentration region, the self-diffusion coefficients of the polyions and the counterions are independent of the concentration. The polyion dynamic behaviour is, in the intermediate- and high-concentration regions, reasonably well described by that of a hard sphere, with a radius of 3.7 nm. A correct prediction for the solvent dynamics is given by the obstruction effect of this hard sphere on the solvent. The relative counterion self-diffusion coefficient is predicted almost quantitatively over the entire concentration range with the Poisson-Boltzmann-Smoluchowski model for the spherical cell, provided that the sphere radius and the number of charges are chosen appropriately (approximately the number of charges in a persistence length). Using this model, the dependence of the counterion self-diffusion coefficient on the ionic strength, polyion concentration and counterion radius is calculated quantitatively over a large concentration range.