  We developed self-consistent dynamical models of stellar systems in the
framework of quasi-linear modified Newtonian dynamics (QUMOND). The models are
constructed from the anisotropic distribution function of Gunn & Griffin
(1979), combined with the modified Poisson equation defining this gravitation
theory and take into account the external field effect. We have used these
models, and their Newtonian analogues, to fit the projected density and the
velocity dispersion profiles of a sample of 18 Galactic globular clusters,
using the most updated datasets of radial velocities and Gaia proper motions.
We have thus obtained, for each cluster, estimates of the dynamical
mass-to-light ratio ($M/L$) for each theory of gravity. The selected clusters
have accurate proper motions and a well sampled mass function down to the very
low mass regime. This allows us to constrain the degree of anisotropy and to
provide, from comparison with stellar evolution isochrones, a
dynamics-independent estimate of the minimum mass-to-light ratio $(M/L)_{min}$.
Comparing the best-fitting dynamical $M/L$ with $(M/L)_{min}$, we find that for
none of the analyzed clusters the two gravity theories are significantly
incompatible with the observational data, although for one of them (NGC 5024)
the dynamical $M/L$ predicted by QUMOND lies at $2.8\sigma$ below
$(M/L)_{min}$. Though the proposed approach suffers from some limitations (in
particular the lack of a treatment of mass segregation), the obtained results
suggest that the kinematics of globular clusters in a relatively weak external
field can be a powerful tool to prove alternative theories of gravitation.
