Diffusion of pentane, cyclohexane, and toluene in nanocomposite films of fumed silica and poly(2,2-bis(trifluoromethyl)-4,5-difluoro-1,3-dioxole-co-tetrafluoroeth ylene) is observed by pulse field gradient NMR. The apparent diffusion constant determined in this experiment depends on the time over which the diffusion measurement is made. The pure copolymer and the nanocomposites based on it are inhomogeneous materials phenomenologically similar to a porous system with the fast diffusion domains having an apparent pore size in the micron size range. In this regard the diffusion can be considered to be anomalous with slopes as low as 0.6 in plots of the logarithm of mean-square displacement vs the logarithm of time at short observation times and at lower silica content. The slower diffusing toluene and cyclohexane are influenced to a greater extent by the inhomogeneous structure when motion is considered over the same time. The addition of nanoparticles increases the diffusion constants of the penetrants substantially, and the diffusion constants from NMR are consistent with diffusion constants determined from desorption experiments. At high nanoparticle concentration, the apparent pore size increases and diffusion becomes closer to Fickian. Rotational motion of cylcohexane is characterized by deuterium spin-lattice relaxation time measurements made as a function of temperature on deuterated cyclohexane in the copolymer/nanoparticle composite. Two minima are present in the spin-lattice relaxation data, indicating the presence of two distinct rotational processes. The two processes are interpreted in terms of the presence of two domains just as in the interpretation of the diffusion data. While an increase in nanoparticle concentration increases the apparent diffusion constants at long times, it does not change rotational motion. The increase in translational mobility is attributed to improved connections between the domains.