In this thesis, x-ray absorption near edge spectroscopy (XANES) experiments were conducted in a range of temperatures upon La1-xCaxMnO3 (x=0.6, 0.8) using synchrotron radiation from the National Synchrotron Radiation Research Center (NSRRC). The O K-edge, Mn L-edge and Mn K-edge absorption spectra at different temperatures were obtained. Further analysis probes the nature of the charge ordering of Mn ions in La1-xCaxMnO3 (x=0.6、0.8) samples. The Mn K-edge spectra were meant to determine the degree of charge disproportion in charge ordered samples. As temperature changed, opposite trends developed in the O K-edge spectra and the Mn K-edge pre-edge spectra of charge ordered La1-xCaxMnO3 (x=0.6, 0.8) and La0.7Ca0.3MnO3 without charge ordering. They were results of the charge ordering. The correlated polaron localizes charge carriers in Mn+3 lattice points and hence results in Jahn-Teller distortion effect. In another series of XANES experiments, the x-ray absorption spectra of standard samples of chromium were obtained. The correlation between the oxidation state and the Cr K-edge absorption edge energy was investigated. A chromium valence state vs. K-edge energy chart was obtained, from which the valence states of Cr in Cr3(PO4)2, Cr2S3, CdCr2S4 and CuCrO4 were determined and verified with L-edge absorption spectrum. The valence of Cr was found to be +6 in CuCrO4, and+2 in Cr3(PO4)2, Cr2S3, CdCr2S4. Furthermore, Cr3(PO4)2 is found to be in high spin state, as its L-edge spectrum highly resembles that of CrF2. This result was testified by the magnetic measurements. Lastly, the valence of Cr was found to be +6 in CuCrO4, which aids the explanation of the charge disproportion of Cu in this compound.