In this study, we use deterministic and stochastic models to analyze the demography of Verreaux's sifaka (Propithecus verreauxi verreauxi) in a fluctuating rainfall environment. The model is based on 16 years of data from Beza Mahafaly Special Reserve, southwest Madagascar. The parameters in the stage-classified life cycle were estimated using mark-recapture methods. Statistical models were evaluated using information-theoretic techniques and multi-model inference. The highest ranking model is time-invariant, but the averaged model includes rainfall-dependence of survival and breeding. We used a time-series model of rainfall to construct a stochastic demographic model. The time-invariant model and the stochastic model give a population growth rate of about 0.98. Bootstrap confidence intervals on the growth rates, both deterministic and stochastic, include 1. Growth rates are most elastic to changes in adult survival. Many demographic statistics show a nonlinear response to annual rainfall but are depressed when annual rainfall is low, or the variance in annual rainfall is high. Perturbation analyses from both the time-invariant and stochastic models indicate that recruitment and survival of older females are key determinants of population growth rate.