An allosteric model is used to describe changes in lifetimes of biological receptor-ligand bonds subjected to an external force. Force-induced transitions between the two states of the allosteric site lead to changes in the receptor conformation. The ligand bound to the receptor fluctuates between two different potentials formed by the two receptor conformations. The effect of the force on the receptor-ligand interaction potential is described by the Bell mechanism. The probability of detecting the ligand in the bound state is found to depend on the relaxation times of both ligand and allosteric sites. An analytic expression for the bond lifetime is derived as a function of force. The formal theoretical results are used to explain the anomalous force and time dependences of the integrin-fibronectin bond lifetimes measured by atomic force microscopy (Kong, F.; et al J. Cell Biol. 2009, 185, 1275-1284). The analytic expression and model parameters describe very well all anomalous dependences identified in the experiments.