The phase diagrams of adsorbed monolayers of D2, H2, O2, and 3He on graphite have been measured by neutron diffraction. H2 and D2-layers have a registered √3 structure at low coverages, and at monolayer completion they have a dense triangular structure, which is incommensurate with the substrate. Between the two densities there is a broad region of coverages where the structure is triangular but the lattice parameter varies with coverage. Adsorbed O2 layers are found to have three distinct phases which are all incommensurate with the substrate lattice. Due to the large absorption cross section of 3He the neutron diffraction measurements from the 3He layers are much more difficult, but both the registered √3 structure and the dense triangular structure near monolayer completion have been observed. Inelastic neutron scattering results are presented for adsorbed H2 and D2 layers.