Large-scale climatic fluctuations, such as the North Atlantic Oscillation (NAO), have been shown to affect many ecological processes. Such effects have been typically assumed to be linear. Only one study has reported a nonlinear relation; however, that nonlinear relation was monotonic (that is, no reversal). Here we show that there is a strong nonlinear and non-monotonic (that is, reversed) effect of the NAO on body weight during the subsequent autumn for 23,838 individual wild red deer (Cervus elaphus) and 139,485 individual domestic sheep (Ovis aries) sampled over several decades on the west coast of Norway. These relationships are, at least in part, explained by comparable nonlinear and non-monotonic relations between the NAO and local climatic variables (temperature, precipitation and snow depth). The similar patterns observed for red deer and sheep, the latter of which live indoors during winter and so experience a stable energy supply in winter, suggest that the (winter) climatic variability (for which the index is a proxy) must influence the summer foraging conditions directly or indirectly.