  The high and very-high energy spectrum of gamma-ray binaries has become a
challenge for all theoretical explanations since the detection of powerful,
persistent GeV emission from LS 5039 and LS I +61 303 by Fermi/LAT. The
spectral cutoff at a few GeV indicates that the GeV component and the fainter,
hard TeV emission above 100 GeV are not directly related. We explore the
possible origins of these two emission components in the framework of a young,
non-accreting pulsar orbiting the massive star, and initiating the non-thermal
emission through the interaction of the stellar and pulsar winds. The
pulsar/stellar wind interaction in a compact orbit binary gives rise to two
potential locations for particle acceleration: the shocks at the head-on
collision of the winds and the termination shock caused by Coriolis forces on
scales larger than the binary separation. We explore the suitability of these
two locations to host the GeV and TeV emitters, respectively, through the study
of their non-thermal emission along the orbit. We focus on the application of
this model to LS 5039 given its well determined stellar wind with respect to
other gamma-ray binaries. The application of the proposed model to LS 5039
indicates that these two potential emitter locations provide the necessary
conditions for reproduction of the two-component high-energy gamma-ray spectrum
of LS 5039. In addition, the ambient postshock conditions required at each of
the locations are consistent with recent hydrodynamical simulations. The
scenario based on the interaction of the stellar and pulsar winds is compatible
with the GeV and TeV emission observed from gamma-ray binaries with unknown
compact objects, such as LS 5039 and LS I +61 303.
