Intra-diffusion coefficients (DSi) have been measured for the ionic liquid constituent ions and aluminium-containing species in aluminium chloride (AlCl3) solutions in the ionic liquids 1-(2-dimethyl-aminoethyl)-dimethylethylammonium bis(trifluoromethylsulfonyl)amide ([C2TMEDA][Tf2N]) and N-butyl-N-methylpyrrolidinium bis(trifluoromethylsulfonyl)amide ([C4mpyr][Tf2N]), to investigate whether spectroscopically detected interactions between the ions and AlCl3 affect these properties. Such electrolyte solutions are of interest for the electrowinning of aluminium. The temperature, composition and molar volume dependences are investigated. Apparent (Vϕ,1) and partial molar (V1) volumes for AlCl3 have been calculated from solution densities. For [C2TMEDA][Tf2N] solutions, Vϕ,1 increases with increasing solute concentration; for [C4mpyr][Tf2N] solutions, it decreases. In pure [C2TMEDA][Tf2N], the cation diffuses more quickly than the anion, but this changes as the AlCl3 concentration increases. In the [C4mpyr][Tf2N] solutions, the intra-diffusion coefficient ratio remains equal to that for the pure ionic liquid and the aluminium species diffuses at approximately the same rate as the anion at each composition. The intra-diffusion coefficients can be fitted to the Ertl-Dullien free volume power law by superposing the iso-concentration curves with concentration dependent, but temperature independent, molar volume offsets. This suggests that they are primarily dependent on the molar volume and secondarily on a colligative thermodynamic factor due to dilution by AlCl3. AlCl3 complexation by [Tf2N]- and [C2TMEDA]+, confirmed by 27Al, 15N and 19F NMR spectroscopy, seems to play a minor role. Our results indicate that the application of free volume theories might be fruitful in the study of the transport properties of ionic liquid solutions and mixtures.