Mixtures of an amphiphilic graft copolymer in water/sodium bis(2-ethylhexyl) sulfosuccinate (AOT)/cyclohexane oil-continuous microemulsions are studied by the PGSE NMR technique and by viscometry. The graft copolymer has an oil-soluble poly(dodecyl methacrylate) backbone and water-soluble poly(ethylene glycol) side chains. Water, surfactant, and polymer self-diffusion coefficients can be measured individually by PGSE NMR. The water and the surfactant self-diffusion coefficients are equal, and both monitor the overall diffusion of the water droplets of the microemulsion. The graft copolymer enhances the microemulsion viscosity (relative increase = 2000), and large viscosifying effects are promoted by increased degrees of grafting, increased polymer concentration, and large water droplets. Systems with high viscosities always display slow polymer self-diffusion. The droplet diffusion is always much more rapid than the polymer diffusion; thus, the polymer molecules do not immobilize the droplets. The results give the following microscopic picture of the mixtures. Polydisperse, but mostly finite, polymer-droplet aggregates coexist with a large fraction (30%) of "free" droplets. The aggregate size varies strongly with the polymer concentration, but only at the highest polymer concentration investigated (28 g/dm3) is there evidence of a fraction of very large (possibly infinite) aggregates. If the polymer/droplet ratio is increased, or if the mixture is diluted by oil, the system responds by inserting more polymer side chains per bound droplet, thus maintaining a high free-droplet concentration.