Feedforward, cascade and feedback interconnections of CNNs were recently studied by Guzelis and Chua ( b i t . j . cir. rheor. uppl., 21, 1-33 (1993)). Their framework was in continuous time with sufficient conditions for global asymptotic and 1 / 0 stability and the relation with classical non-linear control theory such as the Lur'e problem was revealed. In this paper such interconnected CNNs are considered in a discrete time setting. The original system description is brought into a so-called NL, system form using state augmentation. NL,s are a general class of nonlinear systems in state space form with a typical feature of having q 'layers' with alternating linear and static nonlinear operators that satisfy a sector condition. Within NL, theory, sufficient conditions for global asymptotic stability and 1/0 stability are available. The results are closely related to modem control theory ( H , theory and ,u theory). Stability criteria are formulated as linear matrix inequalities (LMIs). Checking stability involves the solution to a convex optimization problem. Furthermore, it is shown by examples that existing interconnected CNN configurations result in q = 1 values. Hence, if one considers the q-value of the NL, as a measure of the complexity of the overall system, such interconnected CNNs still have a low complexity from the analysis point of view. In addition, more complex neural network architectures with 9 > 1 are discussed.