The microstructure and the molecular dynamics of aqueous solutions of an associative polymer (AP), consisting of a polyelectrolyte backbone and attached perfluorocarbon side chains, have been studied by F-19 NMR. The spectral shape and the distributions of the molecular self-diffusion coefficient and of the transverse and the longitudinal relaxation rates along the F-19 spectrum have been measured, together with the magnetic field dependence of the relaxation rates. A comprehensive analysis yields that the spectral lines are broadened by a chemical shift distribution that reflects the distribution of the average hydrophobicity of the environment within the aggregates in which the perfluorocarbon side chains reside. A fraction of the AP chains remain unaggregated with all their side chains immersed in water. As shown by the NMR data, the exchange time of the APs among different states of aggregation is long, > 1 s, while the exchange time of individual side chains among aqueous and hydrophobic environments within the same aggregate is fast, approximately microseconds. Among the aggregates, there is a considerable heterogeneity in the average hydrophobicity. Some implications of the F-19 NMR findings for H-1 NMR studies of APs with hydrocarbon side chains are discussed.