Some recently studied biological noncovalent bonds have shown increased lifetime when stretched by mechanical force. In each case these counterintuitive "catch-bonds" have transitioned into ordinary "slip-bonds" that become increasingly shorter lived as the tensile force on the bond is further increased. We describe analytically how these results are supported by a physical model whereby the ligand escapes the receptor binding site via two alternative routes, a catch-pathway that is opposed by the applied force and a slip-pathway that is promoted by force. The model predicts under what conditions and at what critical force the catch-to-slip transition would be observed, as well as the degree to which the bond lifetime is enhanced at the critical force. The model is applied to four experimentally studied systems taken from the literature, involving the binding of P- and L-selectins to sialyl Lewis(X) oligosaccharide-containing ligands. Good quantitative fit to the experimental data is obtained, both for experiments with a constant force and for experiments where the force increases linearly with time.