The present paper describes the synthesis, characterization of mixed-valence bismuthates with three- or two-dimensional perovskite-like structures and structural criteria that influence superconductivity in these compounds. Single-phase samples of Sr1-xKxBiO3 were prepared for the broad range of K-content: 0.25 less than or equal to x less than or equal to 0.65. For these bismuthates the symmetry of the structure changes from monoclinic to orthorhombic and finally to tetragonal upon increasing the K-content thus resulting in the decrease of the Bi-O distances and reduction of the network distortions. Superconductivity with maximum T-c = 12 K exists in the narrow range (x approximate to 0.5-0.6) within the stability field of the tetragonal phase (0.33 less than or equal to x less than or equal to 0.65), when the three-dimensional octahedral framework has close to the ideal perovskite structure arrangement. The layered type (Ba,K)(3)Bi2O7 and (Ba,K)(2)BiO4 bismuthates belonging to the A(n+1)B(n)O(3n+1) homologous series were investigated. Buckling of the (BiO2) layers in the structure of the n = 2 member occurs due to the ordering of alkaline- and alkaline-earth cations between two independent positions. The formation of the one-layer bismuthate was revealed by Electron Microscopy and XRPD studies. Both types of compounds are considered to be possible candidates for new superconducting materials among bismuthates. (C) 2002 Published by Elsevier Science B.V.