Bleeding order is an order of rules such that one rule destroys the input of another rule.
Consider the following two rules proposed by Schane (1968) for French:
(b) a nasal is dropped in syllable-final position.
To derive the output [bõ] of bon, rule (a) must be applied before rule (b). If (b) would precede rule (a) it would bleed rule (a): the vowel cannot be nasalized anymore and [bõ] could not be derived.