Metal matrix composites, made of Mg or Mg-2wt.%Si matrices reinforced with C or SiC long fibres, were processed by gas-pressure infiltration. Such composites are an advantageous solution for developing light metallic materials, which exhibit simultaneously good mechanical properties and a high damping capacity. For instance C/Mg-Si composites have a specific Young's modulus more than 4 times and a damping capacity 10-100 times higher than steels or aluminium alloys. The thermal behaviour of these materials was investigated by mechanical spectroscopy. Thermal stress relaxation at interfaces gives rise to transient damping, which is interpreted as being due to hysteretic dislocation motion. Hysteretic dislocation motion is also responsible for the mechanical loss background. As this mechanism is not thermally activated, high damping is maintained in a wide frequency and temperature range.