The primary aim of this thesis is to investigate and quantify the self-diffusion processes of gaseous molecules adsorbed in industrially relevant microporous zeolite materials using Pulsed Field Gradient Nuclear Magnetic Resonance (PFG NMR). The main body of this work involves the use of weakly adsorbing hydrocarbon gases (CH4, C2H6 and C3H¬8) adsorbed in a large pore β-zeolite structure. This thesis describes the development of a solely PFG NMR based technique for measuring the molecular displacements of these species at varying length-scales. This enabled the characterisation of self-diffusion regimes across zeolite beds and within individual zeolite crystallites. The characterisation of self-diffusion processes within single zeolite crystallites was critical with respect to accounting for quantitative discrepancies reported in the literature between PFG NMR and alternative measurement techniques. This approach also revealed that the transitions in the Gaussian probability distributions of the molecular displacements in the aforementioned self-diffusion regimes could be recorded by varying the experimental time-scale for observing molecular motion. This technique was extended to characterise the self-diffusion processes of the aforementioned hydrocarbons in small (≤ 1 µm) and large (≥ 15 µm) zeolite crystallites to investigate the dependence of this technique on zeolite geometry. It was found that the self-diffusion coefficients within single crystallites were in good agreement with one another, despite their differing crystallite geometries. This technique was subsequently used to study the self-diffusion behaviour of two-component hydrocarbon gaseous mixtures with differing sorption properties co-adsorbed in β-zeolite. Excellent chemical shift resolution was obtained for chemically similar species using NMR spectroscopy, relaxometry and diffusometry without the use of Magic Angle Spinning (MAS). This connoted that conventional PFG NMR is capable of precisely characterising individual species in real world multi-component systems. This thesis also describes the self-diffusion of ammonia in small pore chabazite structures, which are typically used in Selective Catalytic Reduction (SCR) processes. It was found that the self-diffusion coefficient of this strongly adsorbing species increased with molecular loading up to a certain point. This peculiar behaviour implied a strong concentration and inter-molecular dependence within the zeolite structure. Lastly, the techniques which were developed at high magnetic field strengths (300 MHz) were transferred to a lower field strength (43 MHz) benchtop spectrometer at the Johnson Matthey Technology Centre (JMTC). This describes the first characterisation of mass transport behaviour of weakly interacting sorbates in zeolites using a portable spectrometer. This presents an excellent opportunity for future off-line molecular displacement measurements to be made for complex and real-world systems in a matter of minutes.