  Pulsar bow-shock nebulae are a class of pulsar wind nebulae (PWNe) that form
when the pulsar wind is confined by the ram pressure of the ambient medium, and
are usually associated with old pulsars, that have already emerged from the
progenitor Supernova Remnant (SNR). Until a few years ago these nebulae were
mainly observed as \halpha sources; recently, also non-thermal emission has
been detected. This is the signature of accelerated particles gyrating in a
magnetic field. In the same way as \halpha radiation is a tool for studying the
layer of shocked Interstellar Medium (ISM), the non-thermal radiation might be
used to infer the properties of the shocked pulsar wind. However theoretical
and numerical models have been presented so far only in the hydrodynamical (HD)
regime, while in order to properly model the internal flow structure and the
emission properties of these nebulae a magnetohydrodynamical (MHD) treatment is
required. We present here relativistic MHD (RMHD) axisymmetric simulations of
pulsar wind bow-shock nebulae. The structure and fluid dynamics of such objects
is investigated for various values of the pulsar wind magnetization. Simulated
synchrotron maps are computed and comparison of the emission pattern with
observations is discussed.
