Metal- and ceramic-based composites reinforced with single crystalline oxide fibres promise an essential advance in developing heat-resistant composites. However, to reach a goal of making composites, which would be high creep resistant at very high temperatures and sufficiently damage tolerant at room temperature, a number of scientific and technological problems must be solved. The paper focuses on a particular feature of metal- and oxide-matrix composites, which is an interaction between fibre and matrix yielding considerable changes in microstructure and effective properties of both constituents. A special attention is drawn to a possibility to organize a synergetic fibre/matrix interaction to obtain composites with really new properties.