Fibrous composites are normally fabricated by inserting premade fibres into a matrix and trying to tailor mechanical or physical properties of the material by a proper choice of fibre arrangement, fibre volume fraction, structure and properties of interface, etc. As a rule, this method satisfies all the needs fairly well. But in many cases, particularly when heat-resistant composites are involved, it leads to complications which cause composite experts to refrain from being involved in technically very attractive projects. So the need for alternative methods of composite fabrication obviously exists. The process described here is an example of such an alternative. It is based on the fibres growing from the melt within the volume of the matrix. The matrix should have prefabricated continuous cylindrical channels to be filled with the melt of the fibre material. The process is described using as a model a composite with a molybdenum matrix and single crystalline sapphire fibres. It is shown that the productivity of oxide fibre fabrication based on the process described can be some orders of magnitude higher than that based on the well known Czochralsky's and Stepanov's methods. The strength of the single-crystalline sapphire fibres obtained has been studied, as well as the high-temperature creep strength of composites containing such fibres. Some of the results of these experiments are reported here.