The detection sensitivities of the Alpha Particle X-ray Spectrometer (APXS) instruments on the Mars Exploration Rovers for a wide range of elements were experimentally determined in 2002 using spectra of geochemical reference materials. A flight spare instrument was similarly calibrated, and the calibration exercise was then continued for this unit with an extended set of geochemical reference materials together with pure elements and simple chemical compounds. The flight spare instrument data are examined in detail here using a newly developed fundamental parameters approach which takes precise account of all the physics inherent in the two X-ray generation techniques involved, namely, X-ray fluorescence and particle-induced X-ray emission. The objectives are to characterize the instrument as fully as possible, to test this new approach, and to determine the accuracy of calibration for major, minor, and trace elements. For some of the lightest elements the resulting calibration exhibits a dependence . upon the mineral assemblage of the geological reference material; explanations are suggested for these observations. The results will assist in designing the overall calibration approach for the APXS on the Mars Science Laboratory mission. Copyright 2009 by the American Geophysical Union.