The sexy-sperm hypothesis proposes that polyandrous females will have a selective advantage over monandrous females as their sons will be sired by males with competitively superior sperm and will inherit this trait. Although the good-sperm hypothesis also predicts that offspring will be sired by males with competitively superior sperm, it additionally assumes a positive correlation between offspring sperm quality and the general viability of both sons and daughters. We examined the potential for sexy-sperm and good-sperm processes by exploring the effect of polyandry on offspring sperm quality and immunocompetence in the field cricket, Teleogryllus oceanicus, a species in which sperm viability predicts sperm competitive ability. In the parental generation, females were mated monandrously or polyandrously, where each female received 3 matings. We reared the resultant offspring through to maturity and assayed approximately 10 offspring per family for both sperm viability and immunity. We found that male offspring from polyandrous mothers had higher sperm viability, but that this was not phenotypically associated with male or female offspring condition, as measured by either immune function or ability to survive a bacterial infection. Thus, our data are consistent with a sexy-sperm, but not a good-sperm model in explaining the evolution of polyandry in this species. © 2014 The Author.