Monolithic ceramics are not widely used as structural materials because of their brittleness. Ceramic matrix composites, in which whiskers(1-3) or fibres(4-7) of strong ceramics such as silicon carbide or silicon nitride are embedded in a ceramic matrix, offer improved toughness and strength because the energy of cracks may be dissipated at the whisker/matrix interface. Here we describe a strong ceramic composite with a different kind of microstructure, made by unidirectional solidification of an Al2O3/GdAlO3 eutectic mixture. This composite has a microstructure in which continuous networks of single-crystal Al2O3 and single-crystal GdAlO3 interpenetrate without grain boundaries. Rather than brittle fracture, the material displays plastic deformation at 1,873 K owing to dislocation motion, as in metals. The high strength and resistance to brittle failure of this material at such high temperatures augurs well for applications in mechanical engineering.