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Evolution of the structure of commercially pure copper and Cu-0.8%Hf alloy under high pressure torsion (HPT) is compared. It is demonstrated that doping with Hf affects appreciably a tendency to relaxation processes inherent to copper. Introduction of additional impurities enables to achieve finer fragmentation of structure and increase of microhardness with the strain growth, compared to the commercially pure copper, in which these parameters are weakened by the intensively developing relaxation processes. However, these processes can serve a limiting factor for fragmentation and microhardness increase in the Cu-0.8Hf alloy as well, under the HPT by 5 revolutions of anvils.