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A reaction-diffusion system coupled by two equations subject to homogeneous Neumann boundary condition on one-dimensional spatial domain (0,lπ) with l>0 is considered. According to the normal form method and the center manifold theorem for reaction-diffusion equations, the explicit formulas determining the properties of Hopf bifurcation of spatially homogeneous and nonhomogeneous periodic solutions of system near the constant steady state (0,0) are obtained.