In this study we investigated the microstructural changes after a variety of heat treatments of the quasicrystalline Al–Mn–Be–Cu alloy. In addition, we report on Vickers microhardness measurements and tensile-test results for the same materials. The samples were produced in a conventional manner, i. e., melting in an electrical resistance furnace in air and a gravitational casting process using a round copper die, which was in the form of a tensile-test specimen with a diameter of 5 mm. After the casting, some of the samples were just solution treated (annealed) and then quenched in water, while others were additionally aged (artificially – T6, or naturally – T4) or directly aged after the casting. In comparison to the as-cast state, the Vickers microhardness values of the aluminum-based matrix and the tensile properties of the samples decreased when just the solution treatment, T4 or T6 treatment was performed. The tensile properties also decreased after the heat treatments. A microstructural inspection revealed that the microstructural changes occurred already during the solution treatment, i. e., the formation of the phases Be 4 Al(Mn, Cu) and τ 1 -Al 29 Mn 6 Cu 4 on the approximant H-Al 4 Mn and quasicrystalline i-phase particles' edges and the occurrence of precipitates in the α Al matrix. The precipitates that would additionally contribute to the hardening of the alloy did not form. The directly aged samples showed little or no increase in microhardness values in comparison to the as-cast samples, but possibilities of θ″ precipitates being formed from the already saturated matrix after the casting could not be excluded. After all the heat treatments the quasicrystalline i-phase, as a primary and eutectic phase, was preserved.