1. An increase in the zinc content in alloys based on copper-aluminum increases the thermodynamic stability of high-temperature β-phase as a result of an increase in the electron concentration. 2. A reduction in the cooling rate (water→air) for Cu−Al−Zn (α+β)-alloy with low β-phase stability leads to diffusion decomposition, changing the alloy phase composition and martensite morphology, which markedly increases the ductility properties and sharply reduces the level of mechanical vibration energy dissipation. 3. Quenching in air for β-single-phase Cu−Al−Zn alloys with high β-phase stability is not accompanied by diffusion decomposition and there is a marked increase in damping capacity without a change in mechanical properties.