Ceramic composite materials have unidirectional alignment of the reinforcing fibers. The ratio of the volume of the fiber strands of the reinforcing fibers to the volume of the matrix is at least 0.5. A process for their production involves initially coating the fiber strands or rovings of the reinforcing fibers with a sacrificial polymer. The coated fiber strands are processed with binder resins into unidirectionally reinforced CFK molded parts. The formed CFK bodies are carbonized to form CFC bodies. The CFC bodies are then silicized with liquid silicon. The liquid silicon diffuses into the pores formed in the CFC body and combines there at least partially with the carbon to form silicon carbide. The sacrificial polymer is pyrolized. The ceramic composite materials also can be used in fiber-reinforced ceramic structural parts.