As part of an ongoing program to test Newton’s law of gravity in the low acceleration regime using globular clusters, we present here new results obtained for NGC 6171. Combining VLT spectra for 107 stars with data from the literature, we were able to trace the velocity dispersion profile up to 16 pc from the cluster center, probing accelerations of gravity down to 3.5x10-9 cm s-2 . The velocity dispersion is found to remain constant at large radii (with an asymptotic values of 2.7 km s-1 ) rather than follow the Keplerian falloff. Similar results were previously found for the globular clusters ω Centauri and M15. We have now studied three clusters and all three have been found to have a flat dispersion profile beyond the radius where their internal acceleration of gravity is a0 1.2x10-8 cm s-2 . Whether this indicates a failure of Newtonian dynamics or some more conventional dynamical effect (e.g., tidal heating) is still unclear. However, the similarities emerging between globular clusters and elliptical galaxies seem to favor the first of the two possibilities.