We report on the results from an ongoing programme aimed at testing Newton's law of gravity in the low acceleration regime using globular clusters. We find that all clusters studied so far behave like galaxies, that is, their velocity dispersion profiles flatten out at large radii where the acceleration of gravity goes below 10 8 cm s 2, instead of following the expected Keplerian fall-off. In galaxies this behaviour is ascribed to the existence of a dark matter halo. Globular clusters, however, are not supposed to contain dark matter, hence this result might indicate that our present understanding of gravity in the weak regime of accelerations is incomplete and possibly incorrect.