The high‐arctic tundra ecosystem has the world's simplest vertebrate predator–prey community, with only four predators preying upon one rodent species, the collared lemming (Dicrostonyx groenlandicus). We document the functional and numerical responses of all the four predators in NE Greenland. Using these data, we assess the impact of predation on the dynamics of the collared lemming with a 4 yr cycle and >100‐fold difference between maximum and minimum densities. All predator species feed mostly (>90%) on lemmings when lemming density is >1 ha−1, but the shapes of the predators’ responses vary greatly. The snowy owl (Nyctea scandiaca) is present and breeds only when lemming densities at snowmelt are >2 ha−1, giving rise to a step‐like numerical response. The long‐tailed skua (Stercorarius longicaudus) has a type III functional response and shifts from alternate food (mainly berries and insects) to lemmings with increasing lemming density. The skua surpasses all the other predators in summer by its total response. The type III functional response of the Arctic fox (Alopex lagopus) starts to increase at much lower lemming densities than the responses of the avian predators, but it has only a weak numerical response. Finally, the stoat (Mustela erminea) is the most specialized predator and the only one with a clearly delayed numerical response. According to their specific functional and numerical responses, each predator plays a key role at some point of the lemming cycle, but only the stoat has the potential to drive the lemming cycle. Stoat predation is greatly reduced in the winter preceding the lemming peak, and it reaches a maximum in the winter preceding the lowest lemming summer density. Stoat predation appears to maintain low lemming densities for at least two successive years. Our study provides empirical support for the specialist predator hypothesis about small mammal population cycles.