  Observations of two well known binary systems (LS 5039 and LS I +61 303) with
the satellite and Cherenkov telescopes revealed the broad band $\gamma$-ray
spectra which seems to show two components, the first at GeV energies, showing
exponential cut-off at a few GeV, and the second at TeV energies which does not
fit well to the extrapolation of spectrum from the GeV energy range. We propose
that such two component spectrum is produced by two populations of electrons
which appear within the binary system as a result of acceleration on a double
shock structure separated by a contact discontinuity. Such structure is created
within the binary system as a result of the interaction of the pulsar and
massive star winds. The shocks from the side of the pulsar and the massive star
have different proprieties which allow acceleration of electrons to different
maximum energies. These two populations of electrons produce two component
$\gamma$-ray spectra caused by the Inverse Compton (IC) scattering of stellar
radiation. The example calculations, performed in terms of the anisotropic IC
$e^\pm$ pair cascade model, for the location of the pulsar at the periastron
and apastron passages confirm the high energy emission features observed from
LS I +61 303.
