  Let $\Phi$ and $\Psi$ be frames for $\cal H$ and let $M_{m,\Phi,\Psi}$ be a
frame multiplier with the symbol $m$. In this paper, we restrict our
investigation to show that the operator properties of $M_{m,\Phi,\Psi}$ are
stable under the perturbations of $\Phi$, $\Psi$ and $m$. Also, special
attention is devoted to the study of invertible frame multipliers. These
results are not only of interest in their own right, but also they pave the way
for obtaining some new results for Gabor multipliers which have been studied
mostly by Hans Georg Feichtinger and his coauthors in recent years.
