words) 16Sex-specific selection pressures can generate different phenotypic optima for males and 17 females in response to the current environment, i.e. sex differences in phenotypic plasticity. Less 18 widely appreciated is the possibility that transgenerational plasticity (TGP) can also depend on 19 sex. Sex-specific TGP is potentially of great evolutionary significance, as it is a mechanism by 20 which mothers and fathers can exert different effects on offspring traits and by which potentially 21 adaptive traits can persist selectively across generations via only daughters or sons. Here, we 22 demonstrate that maternally-and paternally-mediated TGP in response to predation risk have 23 largely distinct effects on offspring traits in threespined sticklebacks (Gasterosteus aculeatus). 24 Predator-exposed fathers produced sons that were more risk-prone, while predator-exposed 25 mothers produced more anxious sons and daughters. Further, when combined together, maternal 26 and paternal environments on offspring survival were nonadditive. Such sex-specific effects 27 could occur if predation risk causes mothers and fathers to activate different developmental 28 programs in sons versus daughters. Consistent with this hypothesis, offspring brain gene 29 expression profile depended on whether their mother and/or father had been exposed to risk, and 30 the influence of maternal and paternal environments varied between male and female offspring. 31Altogether these results draw attention to the potential for sex to influence patterns of TGP, and 32 raise new questions about the evolution of plasticity at the interface between sexual conflict and 33 parent-offspring conflict, with paternal strategies, maternal strategies, and offspring counter-34 adaptations all ultimately dictating offspring phenotypes. 35 36 Key words: maternal effect, paternal effect, Gasterosteus aculeatus, phenotypic plasticity, 37 intergenerational plasticity, nongenetic inheritance 38Significance 39 TGP helps organisms cope with environmental change by bridging the gap between 40 within-generational plasticity and long-term evolutionary change. Sex-specific TGP may allow 41 mothers and fathers to selectively alter the phenotypes of their sons and daughters in response to 42 the environment with a greater degree of precision than genetic inheritance and in ways that 43 match the distinct life-history strategies of males and females. By isolating cues coming from 44 mothers versus fathers and separately evaluating phenotypic effects in sons versus daughters, we 45show that interactions between maternal cues, paternal cues, and offspring sex are integral to 46 understanding when and how the past environment influences future phenotypes, and the 47