The major target of this research article is to conduct a new Lyapunov stability analysis of a special model of Cohen-Grossberg neural networks that include multiple delay terms in state variables of systems neurons and multiple delay terms in time derivatives of state variables of systems neurons in the network structure. Employing some proper linear combinations of three different positive definite and positive semi-definite Lyapunov functionals, we obtain some novel sufficient criteria that guarantee global asymptotic stability of this type of multiple delayed Cohen-Grossberg type neural systems. These newly derived stability results are determined to be completely independent of the involved time delay terms and neutral delay terms, and they are totally characterized by the values of the interconnection parameters of Cohen-Grossberg neural system. Besides, the validation of the obtained stability criteria can be justified by applying some simple appropriate algebraic equations that form some particular relations among the constant system elements of the considered neutral neural systems. A useful and instructive numerical example is analysed to exhibit some major advantages and novelties of these newly proposed global stability results in this paper over some previously reported corresponding asymptotic stability conditions.