The growth stresses in a-alumina scales growing on stoichiometric NiAl during oxidation in air at 1100 degrees C have been measured by two X-ray diffraction techniques. the classic rocking technique and a newly developed fixed-incidence multiplane (FIM) technique. The growth stresses were found to be within the experimental uncertainty of the measurements, ie., near zero. Measurement of the residual stresses using an optical-fluorescence spectroscopy (OFS) technique in adherent regions of the scale, after cooling to room temperature, were consistent with the growth stresses having been negligibly small. These measurements contrast with previous measurements of growth stresses in alpha-alumina growing on Fe-Cr-Al alloys, using the FIM technique, which indicated compressive growth stresses on the order of 1 GPa. Possible reasons for these differences are discussed.