We sought to model the mechanism by which leucocytes may be actively repulsed by a β‐chemokine signal. This model is used to interpret an apparent paradox in chemokine biology, whereby high levels of a T‐cell chemoattractant, stromal cell derived factor‐1 (SDF‐1), are present in bone marrow and thymic tissues despite a paucity of mature T lymphocytes in these areas. We postulate the differential involvement in cell migration of the two binding sites on SDF‐1 for its sole receptor, CXCR4, depending on whether high or low concentrations of SDF‐1 are encountered by the cell. Site choice would be mediated by divergent affinities of the two binding interactions. We also propose differential signalling following SDF‐1/CXCR4 interactions on the plasma membrane versus ligand/receptor complexes in endocytic vesicles. Preliminary data showing divergent susceptibility to kinase inhibitors depending on whether a cell is attracted to or repulsed by SDF‐1, are consistent with this model. In terms of physical movement toward or away from a chemokine gradient, we compare the cycling of surface receptors during migration to the caterpillar drive of a tractor, which can change direction simply by altering the direction of rotation of its threads. Finally, the potential clinical implications of concentration‐dependent, chemokine‐based cell attraction and repulsion are discussed.