A review is presented of the potential for very high temperature service of composites consisting of monocrystalline oxide fibres in matrices of the polycrystalline parent oxide. The review is made by specific examination of the stress-strain behaviour and creep behaviour of sapphire fibres in a polycrystalline alumina matrix followed by a review of the creep behaviour of single crystals of other oxides. Certain mixed oxide compounds show considerable promise as reinforcement fibre candidates.