  Let $R=K[x_1,\ldots,x_n]$ be a polynomial ring in $n$ variables over a field
$K$ and $I$ be a matroidal ideal of degree $d$. Let $\astab(I)$ and $\dstab(I)$
be the smallest integers $l$ and $k$, for which $\Ass(I^l)$ and $\depth(R/I^k)$
stabilize, respectively. In this paper, we show that
$\astab(I),\dstab(I)\leq\min\{d,\ell(I)\}$, where $\ell(I)$ is the analytic
spread of $I$. Furthermore, by a counterexample we give a negative answer to
the conjecture of Herzog and Qureshi \cite{HQ} about stability of matroidal
ideals.
