In recent years, the influence of the establishment of long-range order in cubic alloys on the structure of grain boundaries in L12 alloys has been considered. Thus, for example, for the ⅀=5 (310) tilt boundary the various possible structures have been investigated that are generated upon ordering, starting from plausible structures in the disordered state. However, apart from some rough energy estimates based upon nearest neighbour interactions, no reliable energy calculations have been performed of these different possible structures. In this paper, computer calculations based upon interatomic pair potentials constructed in such a way that the L12 structure is stable with respect to disordering, are reported for the ⅀=5 (310) boundary. The relative stability of various possible structures, with associated different boundary compositions, has been investigated.