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The aim of this study is to analyse the uniaxial tensile and creep behaviour of an alumina fibre-reinforced silicon-carbide-matrix composite. The tensile behaviour is elastic-damageable and is related to the extension of fibre/matrix debonding which follows matrix cracking. The uniaxial creep of the composite is characterised by the occurrence of one or two tertiary stages. The first relates to progressive fibre/matrix debonding following matrix cracking which develops during loading. The second tertiary stage appears only at low creep stresses and is related to successive failure of the alumina fibres leading to a non-catastrophic rupture of the composite. The study shows that a conventional Norton analysis of creep can only be considered by taking into account the damage state of the composite at the secondary stage.