Abstract. γ-ray binaries are colliding wind binaries (CWB) composed of a massive star a non-accreting pulsar with a highly relativistic wind. Particle acceleration at the shocks results in emis-sion going from extended radio emission to the γ-ray band. The interaction region is expected to show common features with stellar CWB. Performing numerical simulations with the hydrodynam-ical code RAMSES, we focus on their structure and stability and find that the Kelvin-Helmholtz instability (KHI) can lead to important mixing between the winds and destroy the large scale spiral structure. To investigate the impact of the relativistic nature of the pulsar wind, we extend RAMSES to relativistic hydrodynamics (RHD). Preliminary simulations of the int...