Abstract. In this paper, we generalize the previous formal de nitions of random-self-reducibility. We show that, even under our very general de nition, sets that are complete for any level of the polynomial hierarchy are not nonadaptively random-self-reducible, unless the hierarchy collapses. In particular, NP-complete sets are not nonadaptively random-self-reducible, unless the hierarchy collapses at the third level. By contrast, we show that sets complete for the classes PP and MODmP are random-self-reducible. Key words. random-self-reductions, complexity classes, interactive proof systems, program checkers AMS(MOS) subject classi cations. 68Q05, 68Q15