We prove that the odd nilpotent injectors (a certain type of maximal nilpotent subgroup) f a minimal simple group are all conjugate, extending the result from soluble groups. We also prove conjugacy in GU(\_3\)(q) and SU(\_3\)(q). In a minimal counterexample to the onjecture that the odd nilpotent injectors of an arbitrary ¯nite group are all conjugate we show that there must be a component, which cannot be of type A\(_n\) except possibly 3 ¢ A(\_6\) or 3 ¢ A(\_7\). Finally, we produce a partial result on minimal simple groups for a more general type of nilpotent injector.