We study the asymptotic behavior of a nonhomogeneous semi-Markov system (population) in discrete time. After a series of definitions, lemmas, and theorems, we firstly establish the conditions under which the ergodic behavior of a nonhomogeneous semi-Markov chain exists and then find the limit of the basic matrix of the chain Q(n, s) in closed form. Finally, the existence of the asymptotic population structure of the nonhomogeneous semi-Markov system is studied, and the limit is provided in closed analytic form.
