In socially monogamous species, extrapair paternity typically results from extrapair copulations, but it can also be due to rapid mate switching. Oring, Fleischer, Reed, and Marsden (1992, Nature, 359 (6396), 631–633) proposed a mechanism to explain the occurrence of extrapair paternity in sequentially polyandrous species: sperm stored by females from within-pair copulations with a previous mate could fertilize eggs in the clutch of a subsequent male. Despite being proposed decades ago, evidence for this hypothesis remains limited. We studied social polyandry, extrapair paternity and copulation behaviour in a population of the red phalarope, Phalaropus fulicarius, a nonterritorial, sex role-reversed shorebird, with male-only care, in Utqiaġvik, Alaska. We tested multiple predictions from the ‘sperm storage’ hypothesis. Extrapair paternity occurred in 11% (37/334) of the nests and 4% (42/1182) of the eggs were sired by a male other than the incubating parent. Although a female's initial mate occasionally sired offspring in her next clutch, our results suggest that sperm stored from a previous mate does not play a major role in explaining the occurrence of extrapair paternity in this sequentially polyandrous species. Instead, extrapair paternity was generally due to extrapair copulations by both sexes during the period between pair establishment and early incubation and to rapid mate switching by females in the context of attempts to acquire multiple care-giving males.