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Magnesium matrix composites made of pure (99.98%) magnesium reinforced with long carbon (Mg/C) and stainless steel (Mg/steel) fibers were processed by low pressure infiltration method. Mg/C composites were then oriented from the crystallographic point of view by Bridgman technique and finally three composites were obtained with γ = 0°, 45° and 90° (γ is the angle between the matrix-fiber interface and the normal to the basal plane). The results show that the damping level in the composite for γ = 0° is almost 3 and 7 times higher than that of the composites with γ = 45° and γ = 90°, respectively. From the result analysis it was possible to conclude that the damping originates in the hysteretic motion of dislocations in the magnesium matrix. As such a mechanism is not thermally activated, high damping is observed over a broad frequency range. The complete evolution of the mechanical loss as a function of the vibration amplitude has been measured. The obtained result has been found to be in excellent agreement with the Granato-Lücke model for dislocation breakaway. The fit of the experimental points with the theoretical curve and the straight Granato-Lücke plot confirm that the microstructure evolution is controlled by the breakaway of dislocation segments from randomly segregated point defects (hysteretic damping). According to the Granato-Lücke model the critical stress for the breakaway could be estimated. As a consequence of this analysis, the transient damping due to interface thermal stress relaxation has been interpreted by a model based on a solid friction mechanism. It has been shown that the model of Mayencourt and Schaller justifies the whole mechanical loss behavior. The model predicts two fit parameters C1 and C2, which account for the respective evolution of the mobile dislocation density and interfacial strength. An anomalous behavior is observed for the parameter C2 as well upon heating as upon cooling, which is being reflected in the shear modulus evolution. This anomalous behavior is due to a "bonding-debonding" mechanism at the fiber-matrix interface due to the motion of dislocations, which depends on the orientation of the glide plane. Also, at high temperature, the interface is strong, which helps in creep resistance of the composite, and at low temperature, the interface is weak, which is positive for improving toughness by interface crack deflection.