The properties of p-xylene adsorbed in zeolite Na-Y are studied by molecular simulations. Constrained reaction coordinate minimizations are used to calculate the minimum-energy path for the diffusion. The predicted adsorption site inside the supercage is found to be in good agreement with neutron diffraction results. Extensive molecular dynamics simulations are performed in order to study the behavior of p-xylene as a function of loading at temperatures above 500 K. As important information for the interpretation of experimental data; the distribution of the molecules over the supercages is obtained. Due to the very long simulation runs the diffusion coefficients of p-xylene in the model system are determined with high accuracy. The diffusion coefficients obtained for low sorbate concentration are dose to the largest experimental values, which scatter over more than 2 orders of magnitude. It is found that the diffusivity decreases drastically with increased sorbate loading. Furthermore, the microscopic details of the diffusion process are analyzed by the investigation of site and cage residence times and by orientation correlation functions. The simulations reveal that site-to-site migration inside a supercage is often associated with inversion of the orientation of the aromatic plane.