Membranes obtained by adding small amounts (1 wt %) of nanoplatelets of graphene (G) and graphene oxide (GO) to poly(1-trimethylsilyl-1-propyne) (PTMSP) were fabricated with a simple route, and their gas permeability was measured at 30 degrees C over 9 months. In most cases, variations of PTMSP permeability due to the addition of filler are limited, while the ideal selectivity of CO2/He, CH4/He, and CH4/N-2 is slightly enhanced by addition of filler. Specific measurements indicate that the CO2 and CH4 diffusivity are more strongly affected by addition of graphene than their solubility: such behavior indicates that the filler modifies mainly the microstructure of the polymer rather than its interactions with the gas, as it is reasonable. The most significant quantitative effect observed after filler incorporation is the reduction of PTMSP aging, that was monitored by studying gas permeability after 9 months of aging at room temperature and after annealing at 200 degrees C. The reduction of aging observed after adding graphene is more significant than that obtained with large amounts (up to 20 vol %) of other inorganic fillers, like MgO and TiO2, even though the amount of filler added in this work is small (<1 wt %). Such behavior, coupled to the generally favorable effect of filler on gas permeability and selectivity, makes such materials extremely promising for real applications.