  Let $\mathcal X\rightarrow S$ be a flat family of projective curves over a
complete discrete valuation ring $S$ such that the generic fibre is a smooth
curve of genus $g\geq 2$, the special fibre is an irreducible nodal curve with
a single node and the total space $\mathcal X$ is regular. Let $n$ and $d$ be
integers such that $n\geq 2$ and $(n,d)=1$. There exists a flat family of
varieties $\mathcal M_{_{\tt{GHB,S}}}\rightarrow S$ whose generic fibre is the
moduli space of stable Higgs bundles of rank $n$ and degree $d$ on the generic
curve and the special fibre is the moduli space of stable Gieseker-Higgs
bundles of rank $n$ and degree $d$ (\cite{BBN}). From \cite{H} and \cite{HII},
we know that there exists a canonical symplectic structure on the generic
fiber. Here we prove that there exists a relative logarithmic-symplectic form
on the variety $\mathcal M_{_{\tt{GHB,S}}}\rightarrow S$ which restricts to the
known symplectic structure on the generic fibre and on the special fibre it
induces a logarithmic-symplectic form (in a general sense). We also show that
the special fiber is an example of a singular algebraically complete integrable
system with respect to the log-symplectic structure.
