Results of numerical calculations of the solidification paths of 5000 compositions in the aluminium-rich corner of the AlCuMg system are used to construct the phase diagram for restricted-equilibrium conditions in the range of 0-6 wt% Cu and 0-2 wt% Mg for a cooling rate of 1 K/s at the liquidus. Polythermal projections, temperature-composition sections and the isothermal section below the solidus are shown. The fields of microstructural constituents (primary crystals, binary eutectic mixtures and ternary eutectic) as well as the weight fractions of nonequilibrium phases are given. It is demonstrated that large deviations from equilibrium solidification exist regarding the boundaries of the phase fields and the amount of phases and microstructural constituents, while the differences for varying cooling rates in the range of 0.1 and 10 K/s are less pronounced but still significant. Together with the secondary dendrite arm spacing, the restricted-equilibrium diagram yields the information on the solidification behaviour of Al-rich AlCuMg alloys needed in practical work. © 1990.