An experimentally verifiable model is developed to explain the discrepancy between detected TeV γ-ray pulsed periods and neutron star spin periods in X-ray binary systems. It assumes that the TeV γ-rays are produced at the X-ray period and not on the neutron star itself, but somewhere else in the orbital plane. It was successfully applied to both Cen X-3 and Vela X-1. In the case of Cen X-3, an emission region was identified, with a 99.5% significance. This region trails the neutron star by 70° and is situated between the neutron star orbit and the companion. For Vela X-1 an emission region outside the orbit of the neutron star was found, with a probability for chance occurrence of 4 × 10 -5. This region leads the neutron star by 90°. These detections were used to illustrate the characteristics of the model, especially parameters determining its applicability and possible limitations.