Herein we report on the fabrication and characterization of Mg and Mg-alloy metal matrix composites (MMCs) reinforced with the MAX phases, Ti3SiC2 and Cr2AlC. Pure Mg and Al-containing Mg-alloys with varying Al content (AZ31, AZ61 & AZ91), were pressureless melt infiltrated into 55±1vol% porous MAX preforms. The resulting microstructures and mechanical properties were characterized by X-ray diffraction, scanning electron microscopy, microhardness and uniaxial compression tests. Similar to Ti2AlC/Mg composites increasing the Al content in the matrix enhanced the mechanical properties of the Mg/Ti3SiC2 composites, but had little effect on the properties of the Mg/Cr2AlC composite system. The latter were inferior to those reinforced with the other MAX phases. The Ti3SiC2/AZ91 composite achieved the highest Vickers hardness (1.9±0.1GPa), yield strength (346±4MPa) and ultimate compressive strength (617±10MPa) obtained in this study. All composites exhibited fully and spontaneously reversible hysteresis loops, evidence of energy dissipation, during compression cycling. Having an elastic modulus of ≈ 160GPa, the Ti3SiC2/AZ91 composite may be suited for high specific strength, high damping applications.