The magnetic susceptibility () and magnetization of oxygen ͑O 2 ) monolayers and multilayers physisorped on exfoliated graphite have been investigated in order to elucidate the magnetic and melting transitions in the two-dimensional ͑2D͒ system. An anisotropy of in the dense monolayer phase has been observed below T N ϭ11.9Ϯ0.1 K. The magnetization process shows the precursor of the spin-flop transition, which is estimated to occur in the magnetic-field region 6ϽHϽ7 T at Tϭ5.0 K. These experimental results confirm the existence of magnetic long-range order below T N . The exchange field between nearest-neighbor O 2 molecules in a monolayer is estimated as 70% of that of bulk O 2 . The anisotropy in the fluid-II phase has also been observed, which means that O 2 molecules in this phase have orientational order. In the bilayer region, the second O 2 layer is not only ordered magnetically, but the magnetic ordering of the first layer is also destroyed in a magnetic field when the second layer coverage exceeds 65% of the full coverage of the second layer. These results are discussed in relation to a random-exchange field effect between the first and second layers, which are incommensurate to each other. The feature of melting transitions in the multilayer region is described in terms of surface melting.