Pin-on-disc testing was used to investigate the friction and wear behaviour of a Cu-based metal matrix composite dry sliding against three different martensitic steels. The tests were carried out at two contact pressures (0.5 and 1 MPa) and two sliding velocities (1.57 and 7 m/s), and the results were explained by considering the characteristics of the friction layers formed on the pin and disc surfaces during sliding. At 7 m/s, pin and disc wear was very mild in every condition, because the high flash temperatures achieved during sliding induced intense oxidation of the disc asperities, irrespective of the steel disc compositions. At 1.57 m/s, the steel composition played an important role. When using a heat-treated steel and a conventional martensitic stainless steel, pin and disc wear was by ‘low-sliding speed tribo-oxidation’, regarded as mild wear. However, when using a martensitic stainless steel with a very high Cr-content and a very low C-content, i.e. by a very high oxidation resistance, pin and disc wear was by adhesion/delamination at 0.5 MPa, and thus severe in nature. The results presented herewith clearly suggest the importance of selecting suitable steel counterfaces in the optimization of the tribological systems tribological involving Cu-based metal matrix composites as a mating material.