We analysed two 26–year long (1970 to 1995) time–series on annual population growth rates of Norwegian lemmings (Lemmus lemmus) from Finse, south Norway, using a threshold autoregressive (TAR) approach. We demonstrate that the population dynamics is both phase– and density–dependent. The phase–dependence accounts for the observed nonlinearity. We used the deduced stochastic model structure as a basis for evaluating the dynamic properties of this system. The dynamics is characterized either by limit cycles or chaos (the latter with a strong semi–periodic component). Stochasticity is seen to play an important role in the determination of the periodicity. The ecological implications of these statistical and mathematical results are discussed.