Using the ASCA, XMM-Newton, and Chandra data, luminosity-dependent spectral changes of the ultra-luminous X-ray source (ULX) M 81 X-9 were studied. When the luminosity was below a threshold of ∼1.5×1040 erg s-1, the source consistently exhibited power-law spectra. In contrast, the spectra at higher luminosities were more convex, favoring a multi-color-disk modeling. A p-free disk model with p ∼ 0.6 gave a still better fit to the high-luminosity spectra of M81 X-9, suggesting the presence of a slim disk. Another ULX, NGC 1313 Source B, also showed a similar luminosity-dependent spectral change. These results agree with the ASCA report on the two ULXs in IC 342 (Kubota et al., 2001).