In this thesis we have developed a two prey and one predator population model we have studied the positivity of the solutions of the system and analyzed the existence of various equilibrium points and derive the characteristic equation related to their stability. We have observed that the system is unstable at trivial equilibrium E0 and the axial equilibrium E1. Next we obtain the necessary and sufficient conditions for the existence of interior equilibrium point and local stability of the system at that interior equilibrium . Next we obtain the necessary and sufficient conditions for the existence of equilibrium points E2 and , we have observed that the eigenvalues for the equilibrium E2 have purely imaginary values hence E2 is a center point while x = 0 and the eigenvalues for the equilibrium , has negative real part so the equilibrium , is a stable point while y = 0. Next we have discussed about the stability of delayed model. is the time delay due to gestation . We show there is a critical value of the gestation delay such that the system is stable for lt; and becomes unstable for gt; at the interior equilibrium . By choosing the time delay due to gestation as a bifurcation parameter, we prove the existence of Hopf bifurcations at the equilibrium .