Let G be a semisimple linear algebraic group, ρ:G↪SL(V) a finite-dimensional faithful representation, g≥2 a natural number, and δ a positive rational number. We prove the existence of a compactification of the universal moduli space of semistable principal G-bundles over M¯¯¯¯¯g, provided that δ is sufficiently large, having the following property: the fibers over singular curves are the moduli spaces of δ-semistable singular principal G-bundles.
