In stochastic environments, a change in a demographic parameter can influence the population growth rate directly or via a resulting impact on age structure. Stochastic elasticity of the long-run stochastic growth rate λs to a demographic parameter offers a suitable way to measure the overall demographic response because it includes both the direct effect of changing the demographic parameter and its indirect effect through changes in the age structure. From 25 mammalian populations with contrasting life histories, we investigated how pace of life and population growth rate influence the demographic responses (measured as the relative contributions of the direct and indirect components of stochastic elasticity on λs). We found that in short-lived species, the change in population structure resulting from an increase in yearling survival leads to an additional increase in λs, whereas in long-lived species, the same change in population structure leads to a decrease. Short-lived species thus display a boom-bust life history strategy contrary to long-lived species, for which the long lifespan dampens the demographic consequences of changing age structure. Irrespective of the species’ life history strategy, the change in population age structure resulting from an increase in adult survival leads to an additional increase in λs due to an increase of the proportion of mature individuals in the population. On the contrary, a change in population age structure resulting from an increase of reproductive performance leads to a decrease in λs that is due to the increase of the proportion of immature individuals in the population. Our comparative analysis of stochastic elasticity patterns in mammals shows the existence of different demographic responses to changes in age structure between short- and long-lived species, which improves our understanding of population dynamics in variable environments in relation to the species-specific pace of life.