  In characteristic zero, semistable principal bundles on a nonsingular
projective curve with a semisimple structure group form a bounded family, as
shown by Ramanathan in 1970's using the Narasimhan-Seshadri theorem. This was
the first step in his construction of moduli for principal bundles. In this
paper we prove boundedness in finite characteristics (other than characteristic
2), when the structure group is a semisimple, simply connected algebraic group
of classical type. The main ingredient is an analogue of the Mukai-Sakai
theorem (which says that any vector bundle admits a proper subbundle whose
degree is `not too small') in the present situation.
