A method for the determination of the composition and thickness of thin AI,Ga, -,As films on GaAs substrates by means of energy-dispersive XFA with variable x-ray geometry and with selective excitation of characteristic sample radiations is developed. It can be applied without reference samples. The method was derived from XFA with variable take-off angle. An outline of the theory of the method and the evaluation of measured characteristic signals for an unknown composition x and thickness D of the films is given. This method can be applied to the determination of the compositions and thicknesses of thin multi-element films.