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Long X‐ray observations of bright active galactic nuclei (AGN) show that X‐ray eclipses, with durations from a few hours to a few days, are rather common. This opens up a new window of opportunity in the search for signatures of relativistic effects in AGN: an obscuring cloud covers/uncovers different parts of the accretion disc at different times, allowing a direct check of the expected pattern of disc emission. In particular, the combination of gravitational redshift and relativistic Doppler boosting should imply strong differences between the receding and approaching parts of an inclined thin disc. At present, these effects may be already detectable with a ‘lucky’ XMM–Newton  or  Suzaku  observation of a complete eclipse by a Compton‐thick cloud (a rare, but not impossible‐to‐see event). In the future, higher sensitivity observatories will be able to perform these tests easily on tens of AGN. This will provide a powerful and direct way to test extreme gravity, and to probe the structure of AGN in the close vicinity of the central black holes.

Probing general relativistic effects during active galactic nuclei X‐ray eclipses