Bivalent ligands are increasingly important therapeutic agents. Although the naturally occurring antibodies are predominant, it is becoming more common to combine different antibody fragments or even low molecular weight compounds to generate heterobivalent ligands. Such ligands exhibit markedly increased affinity (i.e. avidity) and target residence time when both pharmacophores can bind simultaneously to their target sites. This is because binding of one pharmacophore forces the second tethered one to stay close to its corresponding site. This ‘forced proximity’ favours its binding and rebinding (once dissociated) to that site. However, rebinding will also take place when the diffusion of freshly dissociated ligands is merely slowed down. The present differential equation-based simulations explore the way both situations affect ligand binding. Both delay the attainment of binding equilibrium (resulting in steep saturation curves) and also increase the target residence time. Competitive ligands are able to interfere in a concentration-dependent manner, although much higher concentrations are required in the ‘forced proximity’ situation. Also, it is only in that situation that the ligand shows increased affinity. These simulations shed light on two practical consequences. Depending on the pharmacokinetic half-life of the bivalent ligand in the body, it may not have sufficient time to achieve equilibrium with the target. This will result in lower potency than expected, although it would have significant advantages in terms of residence time. In in vitro experiments, the manifestation of steep saturation curves and of accelerated dissociation in the presence of competitive ligands could mistakenly be interpreted as evidence for non-competitive, allosteric interactions.