A composite body includes 5 to 40% by mass of SiC whiskers and/or up to 80% by mass SiC lamellae and/or of up to 75% by mass SiC powder, 0.05 to 3% by mass of at least one component selected from the group of Y.sub.2 O.sub.3, SiO.sub.3, MgO, NiO and AlN and/or up to 40% by mass of at least one compound selected from the group of carbides, nitrides or carbonitrides of a metal from one of the Groups IVa, Va, Via of the Periodic Table of elements, and/or up to 40% by mass of at least one oxide of at least one metal selected from the group which consists of the metals of Group IVa of the Periodic Table of elements, 0.05 to 10% by mass of a metal constituent selected from the group which consists of at least one element selected from the group including nickel, cobalt and iron, and of the group which consists of chromium in an amount up to 25% of the mass of the metal constituent with the balance being at least one element selected from the group which consists of nickel, cobalt and iron, and a minimum of 30% by mass Al.sub.2 O.sub.3 to the balance of the body.