  Gamma-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 emission going from extended radio
emission to the gamma-ray band. The interaction region is expected to show
common features with stellar CWB. Performing numerical simulations with the
hydrodynamical 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 interaction
between a pulsar wind and a stellar wind show important similarities with
stellar colliding winds with small relativistic corrections.
