  Let $Y$ be an integral nodal projective curve of arithmetic genus $g\ge 2$
with $m$ nodes defined over an algebraically closed field $k$ and $x$ a
nonsingular closed point of $Y$. Let $n$ and $d$ be coprime integers with $n\ge
2$. Fix a line bundle $L$ of degree $d$ on $Y$. Let $U_Y(n,d,L)$ denote the
(compactified) "fixed determinant moduli space". We prove that the restriction
$\mathcal{U}_{L,x}$ of the Poincare bundle to $x \times U_Y(n,d,L)$ is stable
with respect to the polarisation $\theta_L$ and its restriction to $x \times
U'_Y(n,d,L)$, where $U'_Y(n,d,L)$ is the moduli space of vector bundles of rank
$n$ and determinant $L$, is stable with respect to any polarisation. We show
that the Poincar\'e bundle $\mathcal{U}_{L}$ on $Y \times U_Y(n,d,L)$ is stable
with respect to the polarisation $a \alpha + b \theta_L$ where $\alpha$ is a
fixed ample Cartier divisor on $Y$ and $a, b$ are positive integers.
