  We study stability of noncommutative spaces in matrix models and discuss the
continuum limit which leads to noncommutative Yang-Mills theories (NCYM). It
turns out that most of noncommutative spaces in bosonic models are unstable.
This indicates perturbative instability of fuzzy R^D pointed out by Van
Raamsdonk and Armoni et al. persists to nonperturbative level in these cases.
In this sense, these bosonic NCYM are not well-defined, or at least their
matrix model formulations studied in this paper do not work. We also show that
noncommutative backgrounds are stable in a supersymmetric matrix model deformed
by a cubic Myers term, though the deformation itself breaks supersymmetry.
