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Cellular neural networks (CNNs), as previously described, consist of identical units called cells that are connected to their adjacent neighbors. These cells interact with each other in order to fulfill a common goal. The current methods involved in learning of CNNs are usually centralized (cells are trained in one location) and synchronous (all cells are trained simultaneously either sequentially or in parallel depending on the available hardware/software platform). In this paper, a generic architecture of CNNs is presented and a special case of supervised learning is demonstrated explaining the internal components of a cell. A decentralized asynchronous learning (DAL) framework for CNNs is developed in which each cell of the CNN learns in a spatially and temporally distributed environment. An application of DAL framework is demonstrated by developing a CNN-based wide-area monitoring system for power systems. The results obtained are compared against equivalent traditional methods and shown to be better in terms of accuracy and speed.