NOVELTY - A cathode catalyst contains bronze compound of specific formula.    USE - For electrode assembly for polymer electrolyte fuel cell (claimed) for small power supplies for electronic terminals, motor vehicles, domestic fixed position type co-generation system, mobile telephone, notebook personal computer.    ADVANTAGE - The inexpensive transition metal is used for the cathode catalyst. The cathode catalyst has excellent capability in decreasing over voltage of oxygen reductive reaction. The electrode assembly for polymer electrolyte fuel cell has outstanding electric power generation characteristics. The cathode catalyst is obtained by safe, economical and convenient method without using hydrogen gas.    DETAILED DESCRIPTION - A cathode catalyst contains bronze compound of formula (1): AxMyOz, where M is transition metal, A is metal, m is 2 or more types of mixed valence which consists of highest oxidation number and smallest oxidation number reduced from highest oxidation number, A is unfixed ratio composition, z is greater than 0.1 and less than 1, y is 1 and z is decided by highest valence state that the transition metal (M) takes when y is 1, and x is greater than 0.1 and less than 1. When A is transition metal, the metal A is transition metal different from transition metal (M). INDEPENDENT CLAIMS are included for the following:    (1) cathode catalyst support for polymer electrolyte fuel cells which contains the catalyst supported on carbon particles;    (2) manufacture of cathode catalyst for polymer electrolyte fuel cells. The residue obtained by removing polar solvent from dispersion mixture obtained by disperse-mixing the ion (I) and ion of metal (A), and carbon particles to a polar solvent, is baked in atmosphere(s) selected from inert gas, carbon monoxide and air. The ion (I) is selected from one of ion of transition metal (M), ion of oxide of transition metal (M), ion of nitride of transition metal (M) and ion of sulfide of transition metal (M); and    (3) electrode assembly for polymer electrolyte fuel cells, which has an anode, a cathode and assembly comprising a solid polymer film. A catalyst or a catalyst support is provided in the cathode pole.