Cyclic tests (Bauschinger tests) were conducted at 77 K and at room temperature on the fibre-reinforced material of single crystal Cu with long W-fibres of diameter 20 mum and volume fractions up to 4%. These tests enabled two important contributions to the total strength of the unrelaxed material, the mean stress and the source-shortening stress, to be determined. The mean stress was measured independently, and was found to be a unique function of the numerical applied strain, both at 77 K and at room temperature. The theory for the mean stress describes fairly accurately the behaviour at 77 K for strains below 0.5%. The behaviour at room temperature for strains below 0.4% was not in quantitative accord with the theory, and it is suggested that a reversible relaxation takes place by one or several hindered dislocation processes. The crystallographic features were found to have only a minor influence on the mean stress. The source-shortening stress was estimated as the difference between the total stress and the mean stress; empirical equations showed a dependence on strain to the power and on volume fraction plus a constant: these features are not included in the simple model which however predicts numerical values of the correct order of magnitude. The cyclic hardening rates were large compared to. e.g. pure Cu. and they were constant within the experimental limits. At larger strains, about 0.5% at 77 K and 0.4% at room temperature, irreversible relaxation of Cu-W was initiated by yield of the fibres. This strain for yield is lower than the strain for the unhindered relaxation in the dispersion-hardened material Cu-SiO2.