The demography of livestock populations in Sahelian areas is highly sensitive to periodic stresses generated by climatic fluctuations. A deterministic age-transition matrix model which explicitly accounts for within-year demographic variability was developed. The annual cycle was divided into a number of 24 two-week phases and the annual projection matrix was the product of the 24 projection matrices for each phase. This model was applied to an extensively managed sheep population in North Senegal. Results such as growth rates, age structures and population size projections were compared to field data. We showed that such models can be useful in exploring demographic patterns and thus be powerful descriptive tools for livestock dynamic analysis in periodic environmental variations.