  For a stable irreducible curve $X$ and a torsion free sheaf $L$ on $X$ of
rank one and degree $d$, D.S. Nagaraj and C.S. Seshadri ([NS]) defined a closed
subset $\Cal U_X(r,L)$ in the moduli space of semistable torsion free sheaves
of rank $r$ and degree $d$ on $X$. We prove that $\Cal U_X(r,L)$ is
irreducible, when a smooth curve $Y$ specializes to $X$ and a line bundle $\Cal
L$ on $Y$ specializes to $L$, the specialization of moduli space of semistable
rank $r$ vector bundles on $Y$ with fixed determinant $\Cal L$ has underlying
set $\Cal U_X(r,L)$. For rank 2 and 3, we show that there is a Cohen-Macaulay
closed subscheme in the Gieseker space which represents a suitable moduli
functor and has good specialization property.
