Large-scale seasonal climatic indices, such as the North Atlantic Oscillation (NAO) index or the Southern Oscillation Index (SOI), account for major variations in weather and climate around the world and may influence population dynamics in many organisms. However, assessing the extent of climate impacts on species and their life-history traits requires reliable quantitative statistical approaches. We used a new analytical tool in mark-recapture, the multi-event modelling, to simultaneously assess the influence of climatic variation on multiple demographic parameters (i.e. adult survival, transient probability, reproductive skipping and nest dispersal) at two Mediterranean colonies of the Cory's shearwater Calonectris diomedea, a trans-equatorial migratory long-lived seabird. We also analysed the impact of climate in the breeding success at the two colonies. We found a clear temporal variation of survival for Cory's shearwaters, strongly associated to the large-scale SOI especially in one of the colonies (up to 66% of variance explained). Atlantic hurricane season is modulated by the SOI and coincides with shearwater migration to their wintering areas, directly affecting survival probabilities. However, the SOI was a better predictor of survival probabilities than the frequency of hurricanes; thus, we cannot discard an indirect additive effect of SOI via food availability. Accordingly, the proportion of transients was also correlated with SOI values, indicating higher costs of first reproduction (resulting in either mortality or permanent dispersal) when bad environmental conditions occurred during winter before reproduction. Breeding success was also affected by climatic factors, the NAO explaining c. 41% of variance, probably as a result of its effect in the timing of peak abundance of squid and small pelagics, the main prey for shearwaters. No climatic effect was found either on reproductive skipping or on nest dispersal. Contrarily to what we expect for a long-lived organism, large-scale climatic indexes had a more pronounced effect on survival and transient probabilities than on less sensitive fitness parameters such reproductive skipping or nest dispersal probabilities. The potential increase in hurricane frequency because of global warming may interact with other global change agents (such as incidental bycatch and predation by alien species) nowadays impacting shearwaters, affecting future viability of populations. © 2012 British Ecological Society.