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To solve systems of time-varying nonlinear inequalities, this paper proposes two new types of Zhang neural networks. The first new type of Zhang neural network is based on the conventional Zhang 's neural-dynamics design method, and is termed a conventional Zhang neural network (CZNN). The other one is based on a novel variant of the conventional Zhang 's neural-dynamics design method, and is termed a modified Zhang neural network (MZNN). The theoretical analysis of both CZNN and MZNN is presented to show their excellent convergence performance. Compared with CZNN for solving systems of time-varying nonlinear inequalities, it is discovered that MZNN incorporates CZNN as its special case [i.e., MZNN using linear activation functions (MZNNL) reduces to CZNN exactly]. Besides, MZNN using power-sum activation functions (MZNNP) possesses superior convergence performance to CZNN. Computer-simulation results further demonstrate and substantiate the theoretical analysis and efficacy of both CZNN and MZNN for solving systems of time-varying nonlinear inequalities.