In this article is studied the identifiability of the age-dependent mortality rate of the Von Foerster-Mc Kendrick model, from the observation of a given age group of the population. In the case where there is no renewal for the population, translated by an additional homogeneous boundary condition to the Von Foerster equation, we give a necessary and sufficient condition on the initial density that ensures the mortality rate identifiability. In the inhomogeneous case, modeled by a non local boundary condition, we make explicit a sufficicent condition for the identifiability property, and give a condition for which the identifiability problem is ill-posed. We illustrate this latter case with numercial simulations