  In the current work we investigate the propagation of electromagnetic waves
in the field of gravitational waves. Starting with simple case of an
electromagnetic wave travelling in the field of a plane monochromatic
gravitational wave we introduce the concept of surfing effect and analyze its
physical consequences. We then generalize these results to an arbitrary
gravitational wave field. We show that, due to the transverse nature of
gravitational waves, the surfing effect leads to significant observable
consequences only if the velocity of gravitational waves deviates from speed of
light. This fact can help to place an upper limit on the deviation of
gravitational wave velocity from speed of light. The micro-arcsecond resolution
promised by the upcoming precision interferometry experiments allow to place
stringent upper limits on $\epsilon = (v_{gw}-c)/c$ as a function of the energy
density parameter for gravitational waves $\Omega_{gw}$. For $\Omega_{gw}
\approx 10^{-10}$ this limit amounts to $\epsilon\lesssim 2\cdot 10^{-2}$.
