Molecular simulation studies of methane in silicalite at room temperature are reported. Adsorption isotherms and diffusion coefficients have been calculated for a range of pressures. At low pressures (<20 bar) adsorption is predominantly at specific potential-energy minima in the silicalite channels while at higher pressures adsorption is determined by the total accessible channel volume. Diffusion is found to be strongly anisotropic with the fastest diffusion along the straight channels. Good agreement is obtained with experimental results for orientationally averaged diffusion coefficients. At low pressure, diffusion is well described by a pseudo-Bosanquet formula which identifies two independent contributions to diffusional resistance (from collisions with walls and from intermolecular collisions). At short times significant molecular force correlations arise due to the diffuculty of methane molecules passing each other in the channel intersections of the silicalite lattice. Some preliminary results for butane diffusion coefficients in silicaliate are also reported.