The dynamics of aqueous solutions of a hydrophobically associating polymer is studied by means of pulsed field gradient NMR and dynamic light scattering (DLS). The results from the NMR measurements at higher concentrations reveal an anomalous diffusion behavior. However, when the observation time is increased the classical Fickian diffusion is recovered. These features are discussed in terms of effects of fractal structure and in the light of a coupling model. The concentration dependence of the self-diffusion coefficient is well described by a stretched exponential function. These results constitute the basis for the evaluation of the concentration-dependent coupling parameter. The time correlation function data obtained from the DLS experiments are analyzed, at all concentrations, with the aid of a model, where the initial decay is described by a single exponential followed by a nonexponential relaxation function, which is characterized by a fractional exponential of the Kohlrausch-Williams-Watts type. In the initial stage, an uncoupled relaxation time tau(f) is recognized, which decreases slowly with concentration. The wave vector (q) dependence of tau(f) indicates a crossover from diffusive to a Zimm-like behavior as the concentration increases. At longer times, the analysis yields a mean relaxation time tau(s), associated with the release of coupled clusters. The width of the distribution of relaxation times is given by a parameter beta. This quantity, which is independent of q, decreases from 0.97 at low concentrations to about 0.4 at high concentrations. The parameter tau(s) increases dramatically (several decades) in the studied concentration range. The q dependence of tau(s) is considerably stronger, at higher concentrations, than that of tau(f). All these features can be rationalized in the framework of the coupling model.