Ultrafiltration membranes made of carbon nanotubes are expected to allow gases to selectively pass through them. This selectivity can be predicted from atomistic simulations of the diffusion and adsorption of the gases into and within the nanotubes. The computational nanofluidics of oxygen is therefore been studied with classical molecular dynamics simulations. The interactions in the system are modeled by a short-range reactive empirical bond-order potential coupled to a long-range Lennard - Jones potential. The transport of oxygen molecules for long time periods is characterized by an initial non-equilibrium state followed by an equilibrium state. The non-equilibrium state is characterized by diffusive motion of gas molecules from one end of the nanotube into the vacuum or low-pressure region at the other end of the nanotube, and lasts until the gases are evenly distributed inside the tube. During the non-equilibrium state, the molecules do not exit the nanotube, but rather move back and forth from one end to the other. It is found that this behavior, the time for the level-off, or attainment of equilibrium, and the molecular motions at the openings of the nanotubes are affected by the density (or pressure) of oxygen molecules both inside and outside of the nanotubes. In contrast, at the equilibrium state, for every molecule that enters the nanotube, one molecule exits at the other end.