New measurements of the velocity dispersion of the globular cluster ω Centauri allow us to trace its gravitational potential down to an acceleration of 8×10-9 cm s-2. It is found that the dispersion profile remains flat well inside the tidal radius as soon as the acceleration of gravity approaches a_0, a result that finds its simplest explanation within the context of MOND. A similar behaviour is observed in the globular cluster M15 showing this is not a peculiar feature of ω Centauri. This result is surprising and suggestive of a failure of Newton's law at low accelerations.