Polyethylene single crystals were annealed on various kinds of substrates: a glass plate, evaporated Pt/Pd, evaporated amorphous carbon, HOPG (highly organized pyrolytic graphite), and uniaxially oriented isotactic polypropylene (iPP). Their morphological changes on these substrates by annealing were observed in situ by AFM. On glass and Pt/Pd substrates, polyethylene single crystals started reorganizing from the periphery, accompanying thickening of lamellae, and eventually became molten. Polyethylene single crystals behaved quite differently between on amorphous carbon and on HOPG, which both had the identical chemical constitution: on HOPG, fibrils were produced, extending radially from the center of polyethylene single crystals, while on amorphous carbon, lamellae thickened and melted down without forming any peculiar texture. This difference was caused by the difference in atomic array between the surfaces of HOPG and amorphous carbon. On oriented iPP, a fibrillar texture, with the long axis of fibrils oriented at an angle of 40degrees with the iPP fiber axis, was formed in the process of slow heating. The oriented fibrillar textures that were produced on HOPG and iPP in the heating process were formed under epitaxial control of the surface structure of substrate. The present work showed that oriented crystallization occurred through partial melting in the process of annealing.