Composite oxide fibers were obtained on the basis of various initial mixtures of oxides of aluminium, calcium, barium and yttrium. The fibers contain components that provide the necessary strength and fracture toughness. High strength is provided by alumina. Fracture toughness is mainly determined by the formation of layered components of calcium hexaaluminate or barium hexaaluminate in the fiber structure. Relatively weak planes in the structure of the hexaalumiates play the role of brakes of cracks in composites consisting of non-plastic components. Composites with brittle matrices were made on the basis of these fibers, tests of which showed their “quasiplastic” behavior under load. The strength values in the temperature range of 20–1400 °C and fracture toughness correspond to the requirements for structural materials.