The icosahedral and decagonal aperiodic phases dominate the micro- structures of rapidly solidified A1 -Mn a1 lays because their nuclearion and growth behavior differs substantially from that of the e quilibrium phases. Electron beam surface melting can be used to produce a wide range of solidification conditions, in which the different stages of the nucleation and growth processes can be observed. It is found that the icosahedral phase nucleates abundantly in supercooled A1-Mn melts, and that the decagonal phase is subsequently nucleated by the icosahedral phase. Addition of Si to the Al-Mn alloys suppresses formation of the decagonal phase, but in these alloys the hexagonal p phase can grow rapidly. I - INTRODUCTION In rapidly solidified A1-Mn alloys, aperiodic crystals form by a n ucleation and growth process and the individual crystals reach d iameters of typically a few micrometers before their growth is stopped. Moreover, they are usually embedded in a matrix of f.c.c. Al, and frequently exist as mixtures of the icosahedral (I) and decagonal (2) phases. Although much has been learned from study of such materials, t hey are far from ideal for many measurements. Thus they may be quite suitable for certain TEM studies, somewhat 1 ess satisfactory for examination by x-ray and neutron diffraction and almost u seless for other s tudies such as measure- ment of transport properties. Looked at from a more positive viewpoint, however, studies of the microstructural details of these samples provide us with a great deal of information about the nucleation and growth behavior of the aperiodic phases. It is found that the nucleation behavior of the aperiodic phases is quite different from that of the equilibrium phases of the A1-Mn system, and this difference can account for the dominance of the aperiodic phases in rapidly solidified alloys. In t his paper, the microstructures of rapidly solidified A1 -Mn alloys will be interpreted in terms of conventional metal solidification processes such as nucleation and dendritic growth, and the i mplications w ith respect to crystal- melt interface properties and sample inhomogeneity will be discussed. Most of the conclusions will not depend on the fact that the phases in question have unusual crystal structures.