Past analysis has shown that the population dynamics of Alpine ibex Capra ibex ibex are regulated by both population density and winter snow accumulation. However, recent time series of the ibex counts in the Gran Paradiso National Park, Italy, show interesting trends in comparison with historical snow data: while the winter snow depth has steadily decreased since the beginning of the 1980s, the ibex population experienced rapid growth during the 1980s and the early 1990s, followed by a strong decrease. To explain these dynamics, we built novel age-structured population models in which demographic parameters depended on density and snow depth. They included a non-monotonic effect of snow depth and density on the vital rates, the age and sex structure of the population, and spatial segregation between females and males. Using information criteria (AICc, BIC and SRM), we selected the best models and found that: 1) snow and density interacted in determining the demography of all population sex and age classes, thus confirming that unfavourable climatic conditions intensified the density dependence of the population, 2) the effect of snow was non-monotonic on weaning success and rate of demographic variation of kids, which were maximal for intermediate snow depths, and 3) accounting for spatial segregation between sexes improved the fitting of the models, which suggests that the different use of space made by males and females influenced intraspecific competition. When the selected models were recalibrated using past data and used to simulate recent trends, they underestimated both the rapid growth of the 1980s-1990s and the recent decline of the population. Using the novel sex- and age-structured models, we found that the underestimation of the peak was mainly due to deficiencies of adult demography models, while the overestimation of the recent population abundance was caused by shortcomings in the models of recruitment.