Elastic and anelastic properties of Cu-Al-Ni single crystals (M(s)similar to 370 K) in the beta'(1) martensitic phase have been studied in the temperature range 7-300 K at a frequency of about 100 kHz. Crystals, quenched below M-f or aged in the beta-phase were investigated. For quenched crystals, the Young's modulus exhibits a pronounced anomalous increase in the range 70-230 K, simultaneously with a. significant decrease of the amplitude-independent and amplitude-dependent internal Friction. This anomalous behaviour is attributed to a large contribution of dislocations to the measured Young's modulus and internal friction, due to the existence of an ordered network of partial dislocations in the beta'(1) martensitic phase. Anomalies in the temperature dependence of Young's modulus and amplitude-dependent internal friction are explained by depinning of dislocations from atmospheres of point obstacles under the action of thermal stresses induced within martensitic variants. Ageing in the beta-phase leads to a drastic (up to 30%) decrease of the Young's modulus and an increase of the internal friction in the martensitic phase at room temperature. Only traces of the anomalies are revealed in aged crystals, due to the much smaller concentration of mobile obstacles. Acta Metallurgica Inc. Published by Elsevier Science Ltd.