In this paper, without assuming strict positivity of amplifier functions, boundedness of activation functions, or symmetry of the connection matrix, dynamical behaviors of delayed Cohen-Grossberg neural networks with nonnegative equilibria are studied. Based on the theory of the nonlinear complementary problem (NCP), a sufficient condition is derived guaranteeing the existence and uniqueness of the nonnegative equilibrium in the NCP sense. Moreover, this condition also guarantees the R(+)(n)-global asymptotic stability of the nonnegative equilibrium in the first orthant. The result is compared with some previous results and numerical examples are presented to indicate the viability of our theoretical analysis.