Reflection high-energy electron diffraction (RHEED) and spot profile analysis low-energy electron diffraction (SPA-LEED) were used to study the order-disorder transitions of aluminium films on the Si(111)7X7 surface, up to one monolayer (ML) coverage, deposited by molecular beam epitaxy. The phase transitions at the Al-covered surfaces were studied by analysing the temperature-dependent Bragg reflex intensities and reflex widths within the framework of the theory of phase transitions in two dimensions. Results are presented for Si(111)root 3 root 3X root 3R30 degrees-Al, Si(111)root 7X root 7R19.1 degrees-Al and the Al/Si(111) "gamma phase".