X-ray-absorption measurements have been made at the lanthanide L edges, Sr and Cu K edges in the T*-phase La2-x-yRxSryCuO4 compounds with R=Sm, Eu, Gd, Tb, and Dy. The La and rare-earth x-ray-absorption near-edge (XANES) data and the extended x-ray-absorption fine-structure data both clearly indicate that the R and La ions selectively enter the M' site and M site, respectively. The degree of this site ordering is nearly perfect and is similar for the Sm, Eu, Gd, Tb, and Dy members of this family. The L3 XANES data show that the La, Sm, Eu, Gd, and Dy are trivalent in these compounds, but about 20% of the Tb ions are tetravalent in the Tb material. The Cu K-edge XANES spectra are consistent with a divalent state for copper, and are essentially identical for the as-prepared nonsuperconducting samples and the high-pressure oxygenated superconducting counterparts. This indirectly suggests that the hole carrier in the T*-phase superconductors is largely associated with oxygen atoms as in La1.85Sr0.15CuO4. Based on the results of cation-ordering, cation-valence, and oxygen-content measurements, the superconducting behavior of Sm, Em, and Gd T* phases and the lack of superconductivity in the Tb and Dy compounds are discussed. © 1991 The American Physical Society.