  Let $U^{'s}_L(n,d)$ be the moduli space of stable vector bundles of rank $n$
with determinant $L$ where $L$ is a fixed line bundle of degree $d$ over a
nodal curve $Y$. We prove that the projective Poincare bundle on $Y \times
U^{'s}_L(n,d)$ and the projective Picard bundle on $U^{'s}_L(n,d)$ are stable
for suitable polarisation. For a nonsingular point $x \in Y$, we show that the
restriction of the projective Poincare bundle to $x \times U^{'s}_L(n,d)$ is
stable for any polarisation. We prove that for arithmetic genus $g\ge 3$ and
for $g=n=2, d$ odd, the Picard group of the moduli space $U'_L(n,d)$ of
semistable vector bundles of rank $n$ with determinant $L$ of degree $d$ is
isomorphic to $\mathbb{Z}$.
