  Runaway massive stars are O- and B-type stars with high spatial velocities
with respect to the interstellar medium. These stars can produce bowshocks in
the surrounding gas. Bowshocks develop as arc-shaped structures, with bows
pointing to the same direction as the stellar velocity, while the star moves
supersonically through the interstellar gas. The piled-up shocked matter emits
thermal radiation and a population of locally accelerated relativistic
particles is expected to produce non-thermal emission over a wide range of
energies. We aim to model the non-thermal radiation produced in these sources.
Under some assumptions, we computed the non-thermal emission produced by the
relativistic particles and the thermal radiation caused by free-free
interactions, for O4I and O9I stars. We applied our model to Zeta Oph (HD
149757), an intensively studied massive star seen from the northern hemisphere.
This star has spectral type O9.5V and is a well-known runaway. Spectral energy
distributions of massive runaways are predicted for the whole electromagnetic
spectrum. We conclude that the non-thermal radiation might be detectable at
various energy bands for relatively nearby runaway stars, especially at
high-energy gamma rays. Inverse Compton scattering with photons from the heated
dust gives the most important contribution to the high-energy spectrum. This
emission approaches Fermi sensitivities in the case of Zeta Oph.
