  We analyse the rotation curves and gravitational stability of a sample of six
bulgeless galaxies for which detailed images reveal no evidence for strong
bars. We explore two scenarios: Newtonian dark matter models and MOdified
Newtonian Dynamics (MOND). By adjusting the stellar mass-to-light ratio, dark
matter models can match simultaneously both the rotation curve and
bar-stability requirements in these galaxies. To be consistent with stability
constraints, in two of these galaxies, the stellar mass-to-light ratio is a
factor of ~1.5-2 lower than the values suggested from galaxy colours. In
contrast, MOND fits to the rotation curves are poor in three galaxies, perhaps
because the gas tracer contains noncircular motions. The bar stability analysis
provides a new observational test to MOND. We find that most of the galaxies
under study require abnormally-high levels of random stellar motions to be bar
stable in MOND. In particular, for the only galaxy in the sample for which the
line-of-sight stellar velocity dispersion has been measured (NGC 6503), the
observed velocity dispersion is not consistent with MOND predictions because it
is far below the required value to guarantee bar stability. Precise
measurements of mass-weighted velocity dispersions in (unbarred and bulgeless)
spiral galaxies are crucial to test the consistency of MOND.
