Rapid differentiation and asynchronous coevolution of male and female genitalia in stink bugs.  Despite claims that genitalia are among the fastest evolving phenotypes, few studies have tested this trend in a quantitative and phylogenetic framework. In systems where male and female genitalia coevolve, there is a growing effort to explore qualitative patterns of evolution and their underlying mechanisms, but the temporal aspect remains overlooked. An intriguing question is how fast male and female genitalia may change in a coevolutionary scenario. Here, we apply a series of comparative phylogenetic analyses to reveal a scenario of correlated evolution and to investigate how fast male and female external, nonhomologous and functionally integrated genitalia change in a group of stink bugs. We report three findings: the female gonocoxite 8 and the male pygophore showed a clear pattern of correlated evolution, both genitalia were estimated to evolve much faster than nongenital traits, and rates of evolution of the male genitalia were twice as fast as the female genitalia. Our results corroborate the widely held view that male genitalia evolve fast and add to the scarce evidence for rapidly evolving female genitalia. Different rates of evolution exhibited by males and females suggest either distinct forms or strengths of selection, despite their tight functional integration and coevolution. The morphological characteristics of this coevolutionary trend are more consistent with a cooperative adjustment of the genitalia, suggesting a scenario of female choice, morphological accommodation, lock-and-key or some combination of the three.