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

The surfing effect in the interaction of electromagnetic and gravitational waves. Limits on the speed of gravitational waves