X-ray absorption (XANES and EXAFS) spectroscopic techniques were applied to study the local structural environment of host and dopant cations in Bi-based high-Tc superconductors; the materials studied included BaBiO3, BaBi1-xPbxO3, Ba1-xKxBiO3, Bi2Sr2CuO6, Bi2Sr2CaCu2O8 and Bi2Sr2Ca2Cu3O10. XANES spectroscopy was used to determine the valence state of Bi, Pb and Cu in these materials. In BaBiO3 the valence state of Bi is found to be close to IV both in the pure and doped material, and a disproportionation of BiIV into BiIII and BiV is not indicated by analyses of these data. The valence state of Pb is also found to be IV in BaBi1-xPbxO3. In Bi-based cuprate superconductors, the formal valence states of Bi and Cu are slightly higher than their stoichiometric values of III and II. EXAFS spectroscopy was used to examine the local structure around Bi, Ba, Pb, Sr, Ca and Cu cations in these systems. In the BaBiO3 system, doping with Pb and K results in a decrease in the metal-oxygen bond lengths. The results indicate that the local environment of all cations in the Bi-Sr-Ca-Cu-O system is characterised by substantial static disorder. 73 refs.