Glass‐formation is based on competition between undercooling of the liquid and nucleation of crystal phases, so it is usually obtained around eutectic points. The aim of this work is to analyse the eutectic position and the possible presence of ternary phases in the Cu‐Mg‐Y ternary system, which has been proved to form bulk metallic glasses. The equilibrium crystal phases of the Mg27Cu38Y35 and Mg65Cu25Y10 alloys have been identified, combining experimental data obtained by X‐ray diffraction, scanning electron microscopy and differential scanning calorimetry. New ternary MgCuY, Mg3CuY and Mg4CuY phases are suggested. New ternary phases with composition Mg3CuY (τ4) and Mg4CuY (τ5) are suggested.