Glossina or tsetse flies, the vectors of sleeping sickqess,.form a unique group of insects with remarkable characteristics. They are viviparous with a- slow !hytlynof reppduction (one larva approximately every 10 days) determined by the regular ovulation df alternate ovaries. This unusual physiology enables the age of the females to be estimated by examining the ovaries. The resulting ovarian age structure of tsetse fly populations has been used to develop research into the demography of $etse flies. Several authors have proposed methods of estimating population growth rates from ovarian age distribution data. However, such methods are applicable only when the growth rate (h) is equal to 1 (i.e. the intrinsic rate of increase ris equal to O). In fact, in this type of estimation, the adult survival rate a (or equivalently the mortality rate) cannot be dissociated from the growth rate. Other independently determined demographic parameters must be used to remove this lack of identifiability. We have built a matrix model of the dynamics of tsetse fly populations which enables the growth rate to be calculated from the pupal survival, rate, the pupal period,apd the adult survival rate. Assuming that the age-groups of the population studied have reached a stable distribution, it i calculate the probabilities for the obsed@ sample of belonging to each of the age-groups, to construct a likelihood function and thus to obtain an estimate of the ‘apparent survival rate’ s = a/h If the pupal survival rate and the pupal period are known, a and h can then be calculated from s. The application of this method to data collected for over two annual cycles in a savannah habitat (Burkina-Faso) showed a high overall stability in the populations of Glossinupalpalis gambiensis. Seasonal fluctuations could be easily interpreted as being the result of climatic changes between the dry and rainy seasons.