Semidilute solutions of the flexible highly charged polyelectrolyte sodium poly(styrenesulfonate) have been studied with dynamic light scattering over a wide polyelectrolyte concentration range. To perform a systematic study of the slow mode filters with a relatively large pore size of 0.65 mu m were used. Double-exponential correlation functions were measured. At the lowest polyelectrolyte concentrations the correlation functions became single exponential. The apparent fast and slow diffusion coefficients were determined for three ionic strengths and one molar mass. The fast diffusion coefficient depends on the polyelectrolyte concentration and on the ionic strength but becomes polyelectrolyte concentration independent at a certain high polyelectrolyte concentration. This transition concentration depends on the ionic strength, In the semidilute regime the fast diffusion coefficient follows a power law, with a power law exponent that depends on the ionic strength. The slow diffusion coefficient depends on the polyelectrolyte concentration and on the ionic strength over the whole concentration range studied. Transition concentrations in the static scattering intensity as a function of the polyelectrolyte concentration are also seen in the concentration dependence of the slow diffusion coefficient. The slow mode is interpreted as caused by aggregates or domains that form in semidilute and concentrated solutions. The dimensions of these aggregates, as determined from the angular dependence of the reciprocal normalized scattering intensity, decrease with decreasing polyelectrolyte concentration and increasing ionic strength. Conventional light microscopy shows directly the existence of aggregates.