A method for the measurement of the thickness of thin compound-semiconductor epitaxial films on bulk substrates is presented. It is based on characteristic X-ray intensity measurement using energy-dispersive X-ray spectrometry in a scanning electron microscope. Calibration as necessary for quantitative measurement was performed using bevelled samples as standards. Thereby, we examined layers of thicknesses in the range from a few tens of nm to a few mu m. The results agree with step heights measured by mechanical surface tracing within +/-10%. For thin layers of thickness of a few tens of nm a resolution of the X-ray intensity ratio method around 1 nm was estimated.