Colliding winds of massive star binary systems are considered as potential sites of non-thermal high-energy photon production. This is motivated merely by the detection of synchrotron radio emission from the expected colliding wind location. Here we investigate the properties of high-energy photon production in colliding winds of long-period WR+OB-systems. We found that in the dominating leptonic radiation process anisotropy and Klein-Nishina effects may yield spectral and variability signatures in the gamma-ray domain at or above the sensitivity of current or upcoming gamma-ray telescopes. Analytical formulae for the steady-state particle spectra are derived assuming diffusive particle acceleration out of a pool of thermal wind particles, and taking into account adiabatic and all relevant radiative losses. For the first time we include their advection/convection in the wind collision zone, and distinguish two regions within this extended region: the acceleration region where spatial diffusion is superior to convective/advective motion, and the convection region defined by the convection time shorter than the diffusion time scale. The calculation of the Inverse Compton radiation uses the full Klein-Nishina cross section, and takes into account the anisotropic nature of the scattering process. This leads to orbital flux variations by up to several orders of magnitude which may, however, be blurred by the geometry of the system. The calculations are applied to the typical WR+OB-systems WR 140 and WR 147 to yield predictions of their expected spectral and temporal characteristica and to evaluate chances to detect high-energy emission with the current and upcoming gamma-ray experiments. (abridged)
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