The superconducting oxide BaPb1-xBixO3, discovered in 1975 (ref. 1), is an exotic system having an unusually high transition temperature (T-c) of similar to 12 K, despite a relatively low density of states at the Fermi level. The subsequent prediction(2) that doping the electronically inactive barium donor sites, instead of the bismuth sites, might induce superconductivity with a higher T-c led to the discovery(3,4) in 1988 of superconductivity in the Ba1-xKxBiO3 system (T-c similar to 30 K for x = 0.4). But it remains an open question why many of the superconducting properties of these materials are similar to those of the well-known copper oxide superconductors(5), despite their pronounced structural differences : the former have a three-dimensional bismuth-oxygen framework, whereas the structures of the latter are predominantly two-dimensional, consisting of copper-oxygen planes. Understanding of the copper oxide superconductors has gained immensely from the study of many different superconducting systems, and so it might be expected that the identification of bismuth oxide superconductors beyond the substituted BaBiO3 compounds will prove to be similarly fruitful. Here we report the synthesis of a second family of superconducting bismuth oxides, based on SrBiO3. We show that partial substitution of potassium or rubidium for strontium induces superconductivity with T-c values of similar to 12 K for Sr1-xKxBiO3 (x=0.45-0.6) and similar to 13 K for Sr1-xRbxBiO3 (x = 0.5).