The internal crystallization method for making fibrous composites, which consists of the infiltration of channels made in the matrix with fibre material melt and subsequent crystallization of the melt to produce high-strength fibre, is now applied to fabricate ceramic-fibre/ceramic-matrix composites. Composites thus obtained were not optimized with respect to the microstructure of the fibre, matrix and fibre/matrix interface. However, the possibility of making oxide-/oxide composites by using the internal crystallization method has been demonstrated. Speculations about possible ways of improving mechanical properties of the composites are presented.