The invention relates to a bio and/or synthetic hard foam, especially styrofoam or polystyrene, comprising or consisting of: a) at least one open-cell plastic component, preferably for use as a fire-protective sleeve, wherein the open-cell plastic component is split into a micro-fine, open-cell network structure, and preferably wherein the at least one open-cell plastic component is upgraded with fine mineral substances, and b) at least one closed-cell plastic component, and wherein the closed-cell plastic component b) is embedded into the open-cell plastic component a), and wherein the at least one open-cell plastic component and the at least one closed-cell plastic component form together a cell structure which is at the same time open- and closed-cell. A non-combustible two- or multi-stage composite foam material according to the invention contains for example at least one already expanded very fine component of a sponge-like, open-cell split synthetic foam portion having a thickness of 0.1 mm to 1 mm and a closed-cell expanded bead-like rigid foam plastic portion having a thickness of 2-9 mm with respect to the overall foam matrix component, characterized in that at least one or more mineral or other ground and dried substances are upgraded in two separate stages to form an overall matrix in order to produce according to the invention industrial and craft non-combustible, individual composite foams in the form of dry mixing substances, liquid mixing substances, finished products or other non-combustible mixing substances or special prefabricated elements of all types. All necessary foam can be recycled. Due to the upgrades associated therewith, inflammations are eliminated so that liquefactions, which are also provided by means of deliberate thermal upgradings for example for thermal storage elements, result not in, for example, the formation of burning drips. Along with the other method options, the use of highly loaded recycled polystyrene allows to fall significantly below the load limit values, even by means of unloaded mixing components.