  The rotation curves and the relative mass distributions of the two nearby
Local Group spiral galaxies, M31 and M33, show discrepancies with Modified
Newtonian dynamic (MOND) predictions. In M33 the discrepancy lies in the
kinematics of the outermost regions. It can be alleviated by adopting tilted
ring models compatible with the 21-cm datacube but different from the one that
best fits the data. In M31 MOND fails to fit the falling part of the rotation
curve at intermediate radii, before the curve flattens out in the outermost
regions. Newtonian dynamics in a framework of a stellar disc embedded in a dark
halo can explain the complex rotation curve profiles of these two galaxies,
while MOND has some difficulties. However, given the present uncertainties in
the kinematics of these nearby galaxies, we cannot address the success or
failure of MOND theory in a definite way. More sensitive and extended
observations around the critical regions, suggested by MOND fits discussed in
this paper, may lead to a definite conclusion.
