Abstract: To reduce the mass of internally or externally toothed gears, a thin metal ring having internal or external toothing is made and bonded to a ring of fibrous composite material. Furthermore, to make rings for gears having internal or external toothing, fabric hoses of fibrous composite materials having a fibre orientation of .+-.45.degree. are applied in a number of layers in the peripheral direction to the bottom and side flanks of a U-shaped groove-like depression of a rotating production device; the remaining free space in the interior of the applied fabric hose layers is filled with a unidirectionally wound roving, thereby forming an integral ring after the curing or hardening. Moreover, to make rings for gears having internal or external toothing, two thin-walled rings of fabric laminates serving as shear walls and having a fibre orientation of .+-.45.degree.