Metallic or ceramic hollow spheres are produced by applying a solid layer to a substantially spherical particle of foamed polymer and the coated polymer cores are pyrolyzed with formation of vapor. In order to permit an economical production of the hollow spheres and a wide selection from a wide range of metallic or ceramic materials, the particles consisting of foamed polymer are treated in a state of agitation with an aqueous suspension which contains dissolved or suspended binder and metallic and/or ceramic powder particles, whereby a coating is formed on said polymer particles. The coating is dried, the polymer particles and least part of the binder are subsequently pyrolyzed at temperatures from 400 DEG to 500 DEG C. with formation of vapor while they are agitated and the resulting metallic and/or ceramic hollow spheres are sintered at temperatures from 1000 DEG to 1500 DEG C. while they are agitated.
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