  Let $C$ be an integral projective nodal curve over $\mathbb C$, of arithmetic
genus $g \geqslant 2$. Let $E$ be a vector bundle on $C$ of rank $r$ and degree
$e$. Let $\textrm{Quot}_{C/\mathbb C}(E,k,d)$ denote the Quot scheme of
quotients of $E$ of rank $k$ and degree $d$. We show that
$\textrm{Quot}_{C/\mathbb C}(E,k,d)$ is irreducible for $d \gg 0$.
