Quasicrystalline phases are found in Al–Co–Cu and Al–Co–Ni ternary systems. Knowledge of their phase equilibria is fundamentally important. Equilibrated ternary Al–Co–Cu and Al–Co–Ni alloys are prepared and their phases are determined. Phase equilibria isothermal sections of the Al–Co–Cu system at 800 °C and 900 °C and the Al–Co–Ni system at 900 °C are proposed based on the phase equilibria experimental results of this study, as well as the results in the literature and the phase diagrams of their binary constituent systems. The Al–Co–Cu quasicrystalline phase is in equilibrium with m-Al13Co4, β-Al(Co,Cu) and liquid at both 800 and 900 °C. The Al–Co–Ni quasicrystalline phase is in equilibrium with Al9Co2, Al5Co2, Y1–Al13Co4, Al3Ni2, X and liquid phases at 900 °C. By using the joining test, wetting of Sn-1.3 at.%Cu solder at 250 °C and Ag-39.9 at.%Cu braze at 800 and 900 °C on Al, Co, Cu, Ni, Al-22.67 at.%Co, Al-17.39 at.%Cu, Al-15.29 at.%Ni, Co-41.79 at.%Cu, Co-46.43 at.%Ni, Al–Co–Cu quasicrystal and Al–Co–Ni quasicrystal are systematically examined. It is found the wetting is very poor for both molten Sn-1.3 at.%Cu and Ag-39.9 at.%Cu alloys on substrates of aluminum and its alloys, including Al–Co–Cu and Al–Co–Ni quasicrystals.