  In \cite{nr} Narasimhan and Ramanan and in \cite{desing}, Seshadri
constructed desingularisations of the moduli space $M^{ss}_{_{\text{SL}(2)}}$
of semistable $\SL(2)$-bundles on a smooth projective curve $C$ of genus $g
\geq 3$. Seshadri's construction was even modular and canonical. In this paper,
we construct a smooth modular compactification of the moduli of stable
principal $H$-bundles when $H$ is a simply connected almost simple algebraic
group of type ${\tt B}_{_\ell}, {\tt D}_{_\ell}, {\tt G}_{_2}, {\tt
F}_{_4}~~or~~{\tt C}_{_3}$. These spaces give canonical desingularisations of
the moduli space $M^{ss}_{_H}$ of semistable principal $H$-bundles and thereby,
a comprehensive generalisation of \cite{desing}.
