The trace additions of Ag to binary Al-Mg alloys promote precipitation of a phase in the under-aged condition. The structure of the phase in an Al-10Mg-0.5Ag (mass%) alloy have been characterised using transmission electron microscopy and electron microdiffraction. An icosahedral quasicrystalline phase, which is identified by the electron microdiffraction patterns, has been found in the Al-10Mg-0.5Ag (mass%) alloy after solution treatment, water quenched and then aged during the time between 20 and 40 min. at 513K. The orientation relationship between the quasicrystalline phase and the a - Al matrix is as follows; i5 // <011>a and i3 // <111>a. A uniform distribution of finer-scale (typically 20 nm), faceted precipitate icosahedral quasicrystalline particles was observed within the core of the grains, but the precipitates became coarser (60-80 nm) approaching the grain boundary precipitate-free zone. The quasicrystalline particles contain elements of Al, Mg and Ag. The quasicrystalline precipitate particles, which are the metastable phase, appear to be the primary strengthening phase in the Al-10Mg-0.5Ag (mass%) alloy aged at 513K.