We analyzed 43 yr of live‐trapping data for eight species of small mammals in Algonquin Provincial Park, Ontario. Our primary objective was to test whether complex nonlinear models are necessary to describe dynamics of the Algonquin rodent populations. Variation in abundance among species was related to mean abundance by a simple power function with an exponent of 1.77, implying that population variability did not increase with mean density as much as one might expect for strictly statistical reasons. Time‐series analyses of annual population densities indicated no significant autocorrelation functions for five species. Southern red‐backed voles, red squirrels, and flying squirrels had significant autocorrelations, but only flying squirrels had an autocorrelation function suggestive of cyclic population dynamics. Per capita rates of population growth were density‐dependent in all eight species, although in most cases there was substantial deviation around the fitted regression lines. Response surface models with one‐ and two‐year lags significantly improved the statistical fit to data for three species, but only one of these response surface models was sustainable in the face of realistic stochastic variation in per capita growth. These results suggest that simple logistic models are adequate for predicting the long‐term dynamics of the Algonquin small‐mammal assemblage. All eight species showed evidence of synchronized population fluctuations over time, suggesting trophic linkages due to shared food resources, shared predators, or both.