Although it has been assumed that attraction and repulsion between social individuals constitute a basis for group cohesion, there has been no systematic study of the possible ways in which these tendencies might vary with inter-individual distance (IID), or of associated implications for group structure. In this paper, a family of attraction/repulsion--distance functions is described. Computer simulation was used to examine the effects of each function on group cohesion, as reflected by mean values and variability in IID and group shape. Our results showed that: (a) all models led to stability in group structure, but differed significantly in terms of stable IID and group shape characteristics; (b) cohesion was best served by an upwardly convex behaviour--distance function in which maximum attraction equaled maximum repulsion (and the biological plausibility of this function is discussed); (c) group elongation and variability in mean IID were significantly positively correlated; (d) although dyads maintained an equilibrial separation distance, at which attraction balanced repulsion, in larger groups stable nearest neighbour distances were often less than the equilibrium distance; and (e) individuals needed to monitor and respond to only relatively few of their companions in order to avoid group fragmentation.