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An all-optical neural network is presented that is based on coupled lasers. Each laser in the network lases at a distinct wavelength, representing one neuron. The network status is determined by the wavelength of the network's light output. Inputs to the network are in the optical power domain. The nonlinear threshold function required for neural-network operation is achieved optically by interaction between the lasers. The behavior of the coupled lasers is explained by a simple laser model developed in the paper. In particular, the winner take all (WTA) neural-network behavior of a system of many lasers is described. An experimental system is implemented using single mode fiber optic components at wavelengths near 1550 nm. A number of functions are implemented to demonstrate the practicality of the new network. The neural network is particularly robust against input wavelength variations.