The ability to determine the types and concentrations of acid sites in zeolites and fluid-catalytic cracking systems is important for an increased understanding of structure/performance relationships in these materials. Currently, a variety of thermal methods exist that allow quantitative measurement of the Bronsted acid site concentration. In addition, numerous spectroscopic methods using probe molecules are available for qualitative and quantitative detection of both Bronsted and Lewis acid sites. In studies utilizing solid-state NMR spectroscopy, probe molecules containing P-31 nuclei present substantial advantages over probes isotopically enriched with C-13 and N-15 nuclei. These advantages include increased sensitivity and chemical shift dispersion. While a number of phosphorus-based experiments have probed the interaction of trimethylphosphine with solid acid catalysts, initial studies of the more stable trimethylphosphine oxide (TMPO) have only been reported on amorphous silica-alumina surfaces. We now report the successful completion of TMPO studies of acid sites in several systems including gamma-alumina; HY, USY, and dealuminated Y zeolites; and a silica-alumina catalyst with an aluminum concentration of 13%. Comprehensive and consistent assignments to particular types of sites are made for all resonance lines in the P-31 MAS NMR signals from TMPO. Based on results from dehydroxylated gamma-alumina, new chemical shift assignments are made for the TMPO/Lewis acid complex. The assignments of P-31 resonances from molecules not directly associated with nearby Al-27 nuclei (such as crystalline or physisorbed TMPO species) are supported using H-1/P-31/Al-27 triple-resonance NMR methods. The concentrations of Bronsted acid sites from the NMR results are compared with concentrations obtained from isopropylamine/temperature-programmed-desorption measurements, and substantial agreement between the methods is found.