An icosahedral quasicrystal of composition Al65Mn20Ge15 has been produced by rapid solidification processing. X-ray diffraction reveals this to be a single-phase quasicrystal to the limits of resolution (≤ 5%) of X-ray powder diffractometry. Magnetic susceptibility measurements disclose a large local moment on Mn in this material as determined from fits to a Curie-Weiss law. A 2·10 μB local moment is the largest observed for Mn in Al-based quasicrystalline alloys with similar concentrations (Mn content). D.c. magnetization measurements show a nonlinear field dependence of the magnetization in the field range between 1 and 5 T. A spin glass transition has also been observed at low temperatures and studied using d.c. and a.c. susceptibility measurements and field-dependent specific heat measurements. A spin glass freezing temperature, Tf ~ 8 K, in a 1 T applied field, has been determined from thermomagnetic hysteresis as the temperature at which the field cooled (FC) and zero field cooled (ZFC) d.c. susceptibilities begin to differ. This spin glass transition has been further characterized using a.c. susceptibility measurements where a cusp in the real component, χ´, of the a.c. susceptibility is observed. The cusp position is studied at frequencies of 33·3, 111·1 and 1000 Hz. Finally, specific heat measurements have been performed in fields up to 10 T and in the temperature range between 2 and 20 K. A departure from Debye-like behaviour is observed for T< 10 K and attributed to the spin glass transition. These measurements suggest that less than 1% of Mn atoms participate in the spin glass state in zero field. Larger fields are shown to suppress the number of Mn atoms participating in the spin glass state. © 1992 Taylor & Francis Ltd.