Disclosed are: damage-resistant ECMCs that need to work and remain elastic between minus 120° C. and positive 300° C.; ECMCs that need to be able to contain a flame of 1900° C. for more than 90 minutes; and composite structures, especially highly stressed structures. One of the characteristic problems of ceramic matrices is their fragility. Indeed, when a fracture starts, it propagates easily in the matrix. Disclosed are elastic ceramic matrix composites (ECMCs), for which: the ceramic matrix is split into solid “ceramic microdomains” (CMDs); the CMDs are connected to one another by a dense network of “elastic microelements” (EMEs); and the bonds between the EMEs and the CMDs are strong chemical bonds, preferably covalent.