Abstract The thermodynamic modelling and optimisation of the Al–R, R–Mg and Al–R–Mg (R=Gd, Dy, Ho) systems has been carried out, the Al–Mg system being already optimised in literature. The Compound Energy Formalism (CEF) has been used to describe the thermodynamic functions of either solutions and stoichiometric phases present in the systems. In particular, the order/disorder relation between cI2-W (A2) and cP2-CsCl (B2) phases present in the systems has been taken into account and thermodynamically modelled. Moreover γ-(Mg,Al) and R 5(Mg 1-xAl x) 24 (R=Dy, Ho) phases, related to the cI58-αMn (A12) type structure, have been modelled as different sublattice occupations of the same A12 phase. The thermodynamic modelling of the ternary systems is mainly based on the experimental investigation carried out in our laboratory and reported in a separate paper in this issue . As a result, a complete description of the solid-solid and solid-liquid phase equilibria in the six binary and three ternary systems has been obtained.