We investigate autoreducibility properties of complete sets for \cNEXP under different polynomial reductions.Specifically, we show under some polynomial reductions that there is are complete sets for \cNEXP that are not autoreducible. We obtain the following results:- There is a \reductionptt-complete set for \cNEXP that is not \reductionpbtt-autoreducible.- For any positive integers s and k such that k">2s−1k, there is a \reductionps−T-complete set for \cNEXP that is not \reductionpk−tt-autoreducible.- There is a Turing complete set for \cNEXP that is not \reductionptt-autoreducible.- For any positive integer k, there is a \reductionpk−tt-complete set for \cNEXP that is not weakly \reductionpk−tt-autoreducible.- There is a \reductionp3−tt-complete set for \cNEXP that is not \reductionp3−tt-autoreducible, given that the autoreduction cannot be allowed to ask a query too short or too long. - Relative to some oracle, there is a \reductionp2−T-complete set for \cNEXP that is not \reductionpT-autoreducible. - Relative to some oracle, there is a \reductionpm-complete set for \cNEXP that is not \reductionpNOR−tt-autoreducible.

We will show that settling the question whether every \reductionpdtt-complete set for \cNEXP is \reductionpNOR−tt-autoreducible either positively or negatively would lead to major results about the exponential time complexity classes