According to the results of thermodynamic calculations, it has been determined that the usage of alloys with Hf content near to its maximum possible value solubility in the copper matrix is not appropriate. It is more appropriate to use alloy compositions with lower Hf content. With the help of calculations and analysis of experimental data, it has been established that in order to ensure the thermal stability of SPD-formed structures it is sufficient to obtain a concentration of dissolved in copper matrix Hf of about 0.01 at.%. It has also been shown that the average grain size formed by the SPD is a determining factor in the strength properties of these alloys; an increasing Hf concentration in the copper matrix is not always a condition for higher hardness values. However, higher concentrations of dissolved hafnium in the copper matrix will determine the higher mechanical characteristics of precipitation hardening of the alloys after heat treatment.