This research article considers the problem regarding global robust asymptotic stability of the general type of dynamical neural networks involving multiple constant time delays. Some new sufficient criteria are proposed for the existence, uniqueness and global asymptotic stability of the equilibrium point of this neural network model whose network parameters possess uncertainties. This paper will first address the existence and uniqueness problem for equilibrium points by utilizing the Homomorphic transformation theory. Secondly, by exploiting a novel Lyapunov functional candidate, the sufficient conditions for asymptotic stability of equilibrium points of this class of delayed neural networks will be established. The derived robust stability conditions are expressed independently of the constant time delay parameters and define some novel relationships among network parameters of the considered neural network. Thus, the applicability and validity of the obtained robust stability conditions for delayed-type neural networks can be easily tested. The comprehensive comparisons among the results of the current article and some of previously derived corresponding results will also be made by giving an illustrative numerical example. (C) 2021 Elsevier Ltd. All rights reserved.