The construction and performance of a Pulsed Field Gradient system for use with a commercial, high-resolution, Fourier-Transform NMR spectrometer is described. The self-diffusion coefficient of benzene as measured by the calibrated system is in agreement with the current literature value, within the overall experimental error of the system (±2%). The use of an external lock in conjunction with signal averaging facilitates the measurement of self-diffusion coefficients for solution components in small concentrations. During signal accumulations, the system exhibits freedom from the spin-echo phase and envelope instabilities mentioned as sources of error even in recent publications dealing with the Pulsed Field Gradient technique (e.g. von Meerwall et al., 1979). The ability of the system to investigate dilute solutions is demonstrated by measurements made on 0.5% (w/v) solutions of polystyrene in carbon tetrachloride. Homogeneity coils included in the NMR probe have allowed the self-diffusion coefficients of some single components in multi-component systems to be investigated, and results for the binary system butanol-benzene are presented. Polymer self-diffusion coefficients have been obtained for 110,000 molecular weight random-coil polystyrene in the solvents carbon tetrachloride, deuterated-chloroform and deuterated-toluene. The Pulsed Field Gradient NMR method was used for the measurements, and the polystyrene concentrations ranged from 0.5% (w/v) to 25% (w/v). For each solvent a concentration regime is found in which the de Gennes' polymer self-diffusion scaling law is obeyed; and the upper concentration limit at which this scaling law breaks down is defined. The self-diffusion coefficient of polystyrene in the solvent deutero-benzene has also been determined, and is shown to agree with Forced Rayleigh Scattering self-diffusion results for similar molecular weight polystyrenes in normal benzene. In contrast, values of the self-diffusion coefficient obtained for polystyrene random-coils by calculation from sedimentation data are shown to differ significantly from those directly determined. The mutual diffusion coefficients of the polystyrene solutions have been obtained from Quasi-Elastic Laser Light-Scattering experiments. These mutual diffusion coefficients do not approach the directly measured self-diffusion coefficients even at concentrations where the random-coils are on average well separated. It is proposed that migrating polymers must suffer transient entanglement effects over the experimental time scales employed in the diffusion measurements. Quasi-Elastic Laser Light-Scattering has also been used to measure the diffusion coefficient of polystyrene latex spheres in 0.01M and 0.001M sodium chloride. Experiments were conducted over the latex sphere concentration range 0.004% (w/v) to 4.46% (w/v), and several measurements were also made for low concentrations of latex spheres in triply distilled water. The diffusion coefficient was found to be ionic strength dependent over the entire concentration range studied. Solutions of polystyrene spheres at moderate concentrations exhibit the phenomenon of multiple scattering. The available literature on multiple scattering is reviewed and criteria adopted for the reliable interpretation of data collected during experiments on these solutions. The diffusion coefficients so obtained show substantial agreement with the mutual-diffusion coefficient results of Anderson et al., obtained by a capillary penetration technique. The conclusion reached in this section of the work is that Quasi-Elastic Laser Light-Scattering is able to provide a measure of the mutual diffusion coefficient in the presence of interactions between charged macromolecules. This conclusion is seen to be in accord with earlier laser light-scattering studies on solutions of the protein Bovine Serum Albumin, provided that a reassessment of available mutual diffusion data on these systems is undertaken.