Recent studies have shown that when magnesium is alloyed with particular solute species having very low solid solubilities (< 1%), such as aluminium, copper, tin, zirconium, manganese or silicon, the characteristically high damping is preserved while the mechanical properties are enhanced. Moreover, both damping, and the amplitude dependence of damping, increase with decreasing solute atom concentration. Accordingly, these materials are considered candidates in the fabrication of metal matrix composites (MMCs) for use in large space structures. This paper presents damping data on two magnesium alloys, Mg-0.6%Zr and Mg-1.0%Mn, and a recently developed magnesium MMC, a [0(8)] P55Gr/Mg-0.6%Zr. The alloy data demonstrate the increase in damping and amplitude dependence which accompanies a decrease in alloy concentration. A comparison between the damping of the Mg-0.6%Zr alloy and the [0(8)] P55Gr/Mg-0.6%Zr composite shows that the addition of the strength-enhancing fibres reduces the high damping properties of the matrix.