An experimentally verifiable model is developed to explain the discrep
ancy between detected TeV gamma-ray pulsed periods and neutron star sp
in periods in X-ray binary systems. It assumes that the TeV gamma-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 t
o both Cen X-3 and Vela X-1. In the case of Cen X-3, an emission regio
n was identified, with a 99.5% significance. This region trails the ne
utron star by 70 degrees and is situated between the neutron star orbi
t and the companion. For Vela X-1 an emission region outside the orbit
of the neutron star was found, with a probability for chance occurren
ce of 4 x 10(-5). This region leads the neutron star by 90 degrees. Th
ese detections were used to illustrate the characteristics of the mode
l, especially parameters determining its applicability and possible li
mitations. (C) 1997 Elsevier Science B.V.