This paper studies general Delayed Cellular Neural Networks (DCNNs) with competitive-cooperative configurations. It is demonstrated how such a configuration may be exploited to give a detailed characterization of the fixed point dynamics in DCNNs. Specifically, we show that by dividing the connection weights into inhibitory and excitatory type, it is always possible to embed a competitive-cooperative DCNN into an augmented cooperative delay system, and thus allows for the use of the powerful monotone dynamical system theory. In this way, we derive several simple sufficient conditions on guaranteed trapping regions and guaranteed componentwise (exponential) convergence of DCNNs. The results relate specific decay rate and trajectory bounds to system parameters and are therefore of practical significance in designing a DCNN with desired performance.