In metal matrix composites, temperature changes build up thermal stresses at the ceramic–metal interfaces, which result from the thermal expansion coefficient mismatch between the two phases. Depending on the relaxation mechanisms, such high stresses can degrade the mechanical properties of the composite. During mechanical spectroscopy measurements, thermal stress relaxation gives rise to an additional transient mechanical loss response. In order to interpret the dominant mechanism of stress relaxation, different models have been proposed, which relate the transient loss with interface debonding, growth of a plastic zone around the fibres, or creation and motion of dislocations. In the case of the magnesium-based composites, a nonlinear relation is observed between the transient loss and the measurement parameters, which cannot be explained by the existing models. In order to interpret the mechanism of stress relaxation in these composites, a new theoretical approach has been developed. The model takes into account a relaxation mechanism due to the motion of the existing dislocations. It allows one to distinguish between the case where the dislocation motion is controlled by a viscous force such as due to the dragging of solute atoms, and the case where the motion is controlled by a solid friction mechanism such as the breakaway from pinning points. In the case of the magnesium-based composites, the model allows one to conclude that the dominant mechanism of thermal stress relaxation is the motion of existing dislocations, which is controlled by a solid friction mechanism.