Molecular simulations were performed to investigate the adsorption and diffusion properties of methane and carbon dioxide in carbon nanotubes (CNTs) with preadsorbed water at 300 K and pressures up to 40 bar. Our results show that, at low pressures, a high uptake of methane and carbon dioxide is obtained in relatively small pores, and the presence of water enhances the adsorption of carbon dioxide in CNTs with large diameters. The effect of the preadsorbed water is more pronounced on the mobility of methane than that of carbon dioxide. Importantly, at high water contents, we see that the mobility of methane is a nonmonotonic function of the nanotube diameter. This is probably due to the splitting of the water clusters in the small pores which may lead to a faster diffusion process. Simulations were also performed for the methane/carbon dioxide mixture in CNTs with preadsorbed water. Here, the overall adsorption and diffusion properties are similar to those observed for the methane/water and carbon dioxide/water mixtures in CNTs. The adsorption selectivity of carbon dioxide over methane increases with water content which may be because of the relatively stronger water-carbon dioxide interactions. A significant result is that the mobility of methane in the CNTs decreases with decreasing bulk mole fraction of methane. In general, this decrease is more pronounced at higher loadings of methane and lower water contents. However, the presence of methane has less effect on the diffusion properties of carbon dioxide in the CNTs. These results may be explained by the preferential adsorption of carbon dioxide over methane in the CNTs. Furthermore, these simulated adsorption isotherms and diffusivity results are in reasonable agreement with the theoretical predictions based on the ideal adsorbed solution theory and the Krishna and Paschek approach, respectively.