Dissertation (MSc Mathematics)The study of predator prey model with immigrant prey with and without harvesting has received great attention from both theoretical and mathematical biologists and has been studied intensively and extensively. Different literatures on interaction between species have been surveyed. In this document we establish sufficient stability criteria, criteria for the existence of periodic solution and Hopf bifurcations of a predator prey systems with immigrant prey without and with harvesting of predator. The ecological system in nature can be balanced by introducing an immigrant prey to ensure existence of both preys and predators. Harvesting of predator also can be used as a stabilizing factor as far as they depend on prey for their survival. The approach involves the use of software program (mat lab) in analyzing Equilibrium points, periodic solutions, Hopf bifurcations and its related theorems.