Non-negative matrices arise naturally in population models. In this thesis, we first study Perron-
Frobenius theory of non-negative irreducible matrices. We use this theory to investigate the asymptotic
behaviour of discrete time linear autonomous models. Then we discuss an application for this in age
structured population. Furthermore, we study Liapunov stability of a general non-linear autonomous
model. We consider a general nonlinear autonomous model that arises in structured population.
We assume that the associated nonlinear matrix of this model is non-increasing at all density levels.
Then, we show the existence of global extinction. In addition, we show the stability condition of the
extinction equilibrium of the this model in the Liapunov sense.
