Periodic solutions of reaction-diffusion systems with time delays are investigated. The upper and lower control function of nonmonotone reaction term is constructed. It is showed that the function satisfies a global Lipschitz condition and quasimonotone. A sort of effective method of studying differential equation with nonmonotone reaction term is gained. It is shown that periodic solutions of this system exist when reaction-term is not monotone and the boundary value system has a pair of coupled to-upper and lower solutions.