Akinwande, N. I.Somma, Samuel Abu2025-04-140205-04-102348-5736http://repository.futminna.edu.ng:4000/handle/123456789/656Abstract: In this work, we present a result in the form of a lemma which we name COA-Sowunmi’s Lemma, its proof and application to the stability analysis of the transcendental characteristics equation arising from the perturbation of the steady state of the non-linear age-structured population model of Gurtin and MacCamy [11]. Necessary condition for the asymptotic stability of the equilibrium state of the model is obtained in the form of constrained inequality on the vital parameters of the model. The result obtained is then compared with that of an earlier work by the [4].enCharacteristic equationSteady or Equilibrium stateStabilityArticle