Temporal autocorrelation in demographic processes is an important aspect of population dynamics, but a comprehensive examination of its effects on different life-history strategies is lacking. We use matrix population models from 454 plant and animal populations to simulate stochastic population growth rates (log λs) under different temporal autocorrelations in demographic rates, using simulated and observed covariation among rates. We then test for differences in sensitivities, or changes of log λs to changes in autocorrelation among two major axes of life-history strategies, obtained from phylogenetically informed principal component analysis: the fast-slow and reproductive-strategy continua. Fast life histories exhibit highest sensitivities to simulated autocorrelation in demographic rates across reproductive strategies. Slow life histories are less sensitive to temporal autocorrelation, but their sensitivities increase among highly iteroparous species. We provide cross-taxonomic evidence that changes in the autocorrelation of environmental variation may affect a wide range of species, depending on complex interactions of life-history strategies.