The feasibility of using neural networks in a practical halftoning application is considered. The cellular neural network (CNN) architecture is chosen for its proven implementability in VLSI and high-speed operation. Since both the CNN and halftoning have a geometrically local character, the CNN provides a natural implementation. The CNN template weights are derived by analogy to the well-known error diffusion algorithm for halftoning. Some limitations of the neural network approach are analyzed, providing an advance in designing template weights over previous methods. These limitations are shown to be especially critical in the case of the small interconnection neighbourhoods needed for efficient implementation. The design criteria are validated by direct simulation. The resulting halftones are shown to be more faithful reproductions of the original than those produced by the error diffusion algorithm. It is suggested that a CNN with optical inputs could provide a high-speed scanner/halftoner for applications such as facsimile.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>