Thermodynamic calculations, scanning electron microscopy, X-ray diffraction analysis, and differential scanning calorimetry have been used to study the phase composition of a Al–Zn–Mg–Cu–Zr alloy that is rich in copper, which was additionally alloyed with yttrium or erbium. There are (Al), T, Al8Cu4Y, and AlMgY phases of solidification origin in the AlZnMgCuZrY alloy. The erbium-bearing AlZnMgCuZrEr alloy contains three additional intermetallic phases in addition to the T phase: two intermetallic phases with a composition close to the Al8Cu4Er phase and one of the Al3Er composition. One of the Al8Cu4Er-phase particles contains approximately 2 wt % Fe. Aging at 150°C led to a greater increment in the hardness of the erbium alloy, while the hardness level achieved is the same for all alloys under study. Overaging at 210 and 250°C takes place significantly earlier in the alloy without yttrium and erbium additives, given the same level of hardening. Taking the fact into account that the kinetics of aging depend mainly on the (Al) composition, the differences in kinetics in the alloys with additions can be explained by dispersoids formed during homogenization before quenching and the solid solution depleted of the main elements (zinc, magnesium, and copper). The yield strength of the alloys with yttrium and erbium additives is insignificantly lower at high temperatures, which is likely due to the lower alloying of the aluminum matrix. However, these alloys are of a better technological effectiveness at casting.