International audienceThermodynamic (specific heat, reversible magnetization, tunneling spectroscopy) and transport measurements have been performed on high quality K, Ba BiO3 single crystals. The temperature dependence of the magnetic field HCp corresponding to the onset of the specific heat anomaly presents a clear positive curvature. HCp is significantly smaller than the field HD for which the superconducting gap vanishes but is closely related to the irreversibility line deduced from transport data. Moreover, the temperature dependence of the reversible magnetization presents a strong deviation from the Ginzburg-Landau theory emphasizing the peculiar nature of the superconducting transition in this material