Angle-dependent x-ray photoelectron spectroscopy (AD-XPS) measurements have been carried out on thin aluminium oxide layers formed on pure aluminium by oxidation in oxygen at 25-degrees-C and at 250-degrees-C. The amounts of oxygen of the oxide overlayers were measured by nuclear reaction analysis (NRA). The equivalent thicknesses of the oxide layers were 14 angstrom and 21.5 angstrom for the oxides formed at 25-degrees-C and at 250-degrees-C, respectively. The AD-XPS measurements were carried out in the range of take-off angles 12-122-degrees. The signals emitted by Al3+ in the oxide and by Al(m) in the metal versus take-off angle can be, within experimental error, fitted by an exponential function in the range of take-off angles approximately 30-120-degrees. This confirms the applicability of an exponential law for the attenuation of photoelectrons for the studied system in the range of take-off angles approximately 30-120-degrees. The AD-XPS measurements were used to determine the attenuation lengths of the electrons emitted by aluminium (kinetic energy approximately 1180 eV) in the oxide (lambda(ox)) and in the metal (lambda(m)). The attenuation lengths derived from the experiments are: lambda(ox) = 20 angstrom and lambda(m) = 18 angstrom. These values are lower than the theoretical inelastic mean free paths owing to the contribution of elastic scattering. For the lowest investigated take-off angles (<30-degrees) the measurements deviate from the exponential law. The deviation is attributed to the effects of elastic scattering and of the angle of acceptance of the photoelectrons. As a complement to this work, an intercomparison of AD-XPS measurements was performed in four laboratories on the two reference samples. In the range of take-off angles 40-120-degrees, the results can be fitted by the exponential law for the attenuation of the photoelectrons. However, differences of 10-20% were observed in the apparent overlayer thickness. Careful analysis of the data revealed that this was primarily caused by a systematic error introduced in the peak fitting when a symmetrical peak is used, instead of an asymmetrical peak, for the Al(m) signal.