Many-body, long-range potentials of a Finnis-Sinclair type are formulated for the atomistic description of binary f.c.c. metallic alloys. These potentials are generalizations of the scheme constructed by Sutton and Chen (1990), for the atomistic modelling of f.c.c. elemental metals. The parameters for the alloy potentials are obtained directly from the parameters for the elemental metals, without any further adjustable fitting. Lattice parameters, elastic constants and enthalpy of formation of 45 binary, random f.c.c. alloys are calculated.