Mumba rockshelter is a key archaeological site for the Middle and Later Stone Age occupation of East Africa, but its chronology has remained unresolved. We report the results of a dating study, focussing on the characterisation of the optically stimulated luminescence (OSL) and infrared stimulated luminescence (IRSL) properties of quartz- and potassium-rich feldspar grains. Quartz has previously proven troublesome for dating in East Africa. We identified five general types of quartz grain behaviour, based on the shapes of their OSL decay and dose–response curves. Dose recovery experiments and measurement of the natural samples revealed particular problems with quartz grains that had hyperbolic dose–response curves, low characteristic saturation doses and anomalously large changes in sensitivity between regenerative-dose cycles. The use of pulsed irradiation during measurement and standard and additional quality-assurance criteria during data analysis reduced the number of grains that suffered from these problems. We applied these procedures to individual grains of quartz from eight samples and, using appropriate statistical models, identified post-depositional mixing in three samples. The remaining samples had scattered equivalent-dose distributions typical of quartz grains that had received variable beta dose rates during burial. Stratigraphically consistent OSL ages were obtained for all but the deepest sample. Feldspar ages were estimated for the latter sample and three other samples, using the elevated temperature IRSL signal that exhibited low rates of anomalous fading. Fading-corrected feldspar ages for the latter three samples are consistent with their single-grain quartz ages, but single-grain dating is needed to address problems of post-depositional mixing.