Low density permeations of some gases (He, H-2, N-2, CH4, CO2 and CF4) through micro- and mesocarboneous pores were investigated using Knudsen and Oscillator models. Lennard-Jones model in single layer pores was used to simulate the gas-solid interactions in the Oscillator model. The effects of the pore radius as well as the molecular size and the temperature on the pore diffusivity and the activation energy were studied. The Monte Carlo simulation was then performed to calculate the permeability of these gases in three-dimensional cubic networks of different connectivities (2.5-6) and different pore size distributions (r(a) = 2.74 and 6.95 nm). It was shown that for networks with larger pores there is a minor difference between the two models, while a large discrepancy exists in networks with fine pores. Both models tend to have the same permeability as the coordination number decreases. To investigate the accuracy of the models, the simulation results were compared with the experimental selectivities of some pure gases in two different membranes extracted from the literature. It was shown that the Oscillator model can better predict the experimental data in the membranes of smaller pores (i.e. r(a) = 2.74 nm). However, both models were comparable in membranes of larger pores (r(a) = 6.95 nm). The capability of the models to predict the activation energy of the diffusion was also studied.