In this paper a system of two coupled differential equations with two parameters is analyzed. Using linear stability analysis, the equilibrium points of the system and their stability are determined depending on two parameters. For one of the equilibrium points the possibility of a Hopf bifurcation is examined. Applying algorithm for Hopf bifurcation, conditions under which a Hopf bifurcation occurs are derived for this equilibrium point. The nature of the bifurcation—whether supercritical or subcritical—is determined. These results provide insights into the system's qualitative behavior and parameters impact on character and stability of the equilibrium points.