This research work studies stability problems for more general models of neutral-type neural systems where both neuron states and the time derivative of neuron states involve multiple delays. Some new sufficient criterion is presented, which guarantee the existence, uniqueness, and global asymptotic stability of equilibrium points of the considered neural network model. These obtained stability conditions, which can be applied to some larger classes of general neural network models, are based on the analysis of a new and improved suitable Lyapunov functional. The proposed conditions are independent of time delay parameters and can be easily justified by examining some certain relationships among the relevant neural network parameters. This paper also shows that the obtained stability criteria can be considered as the generalization of some previously reported corresponding stability conditions for neural networks, including multiple time delay parameters.