The method of Kaufman and coworkers is used to provide an estimate of isothermal sections of the Al--Li--Mg system. One starts by calculating the lattice stability of the constituents, the binary interaction coefficients and the binary compound parameters. In the computations, thermodynamic data, when available, were coupled with measured phase diagrams to provide thermodynamically self-consistent liquidus and solidus curves for the binary systems. Standard enthalpies of formation and entropies of formation were calculated for the reported compounds. The binary system Li--Mg illustrates the use of such calculations in selecting the most reliable representation of the phase diagram. The calculated binary data were used to compute the phase diagram of Li--Al--Mg, assuming that no ternary compounds exist. 4 tables, 7 figures, 29 references. (GHT)