The nucleation and growth of quasicrystalline thin films during sequential vapor deposition of aluminum and manganese on various substrates have been studied at temperatures between 530 and 650 K. The films were analyzed by transmission electron microscopy, electron diffraction, energy dispersive x-ray analysis, replica techniques, and Auger depth profiling. The quasicrystalline phase is identified as icosahedral. It nucleates on the surfaces of the Al films. There is no indication of substantial bulk Mn diffusion. The growth process is governed by diffusion of Al to the quasicrystal surface where it reacts with the incident Mn.