Because of a rapidly changing climate, the need to understand how populations respond to varying climatic conditions has become increasingly important. Using long-term data from an unhunted population of Alpine chamois (Rupicapra rupicapra) and autoregressive time series models we investigated the extent to which the population demography was affected by local climate. Because density and weather are likely to operate differently on various sex–age categories, anticipated effects were assumed to vary among categories. Generally, elevated densities in 1 year negatively influenced the subsequent change in population size. Severe snow conditions during late winter negatively affected total population growth, and growth of the male, yearling, and juvenile segments of the population. A lagged effect of early winter snow on the change in animal numbers was demonstrated for females. Winter temperatures positively affected the growth rate of juveniles, whereas they appeared to have negative consequences for male and yearling growth rates. The juvenile–female ratio was negatively affected by the current female density, but did not respond to the various climate variables. Winter survival of juveniles was negatively influenced by the juvenile number during the preceding summer and harsh snow conditions during early winter. Our results indicate that winter climate shapes the demography of Alpine chamois. Particularly, winters with a lot of snow might have long-lasting consequences for the population. Considering the juveniles, lagged effects apparently operate through the body condition of their mothers. The conflicting effects of temperature on the different sex–age categories make the direction of expected population response to global warming difficult to predict.