A commonly reported pattern in large herbivores is their propensity to irrupt and crash when colonizing new areas. However, the relative role of density-dependence, climate, and cohort effects on demographic rates in accounting for the irruptive dynamics of large herbivores remains unclear. Using a 37-yr time series of abundance in a mouflon Ovis aries population located on Haute Island, a sub-Antarctic island of Kerguelen, 1) we investigated if irruptive dynamics occurred and 2) we quantified the relative effects of density and climate on mouflon population dynamics. Being released in a new environment, we expected mouflon to show rapid growth and marked over-compensation. In support of this prediction, we found a two-phase dynamics, the first phase being characterised by an irruptive pattern best described by the θ-Caughley model. Parameter estimates were rm=0.29±0.005(maximum growth rate), K=473±45 (carrying capacity) and S=2903±396 (surplus) mouflon. With a θ=3.18±0.69 our model also supported the hypothesis that density dependence is strongest at high density in large herbivores. The second phase was characterised by an unstable dynamics where growth rate was negatively affected by population abundance and winter precipitation. Climate, however, did not trigger population crashes and our model suggested that lagged density-dependence and over-grazing were the probable causes of mouflon irruptive dynamics. We compare our results with those of Soay sheep and discuss the possibility of a reversible alteration of the island carrying capacity after the initial over-grazing period.