A new optical neural-network concept using the control of the modes of an injection laser by external feedback is described by a simple laser model. This approach uses the wavelength dispersed longitudinal modes of the laser as neurons and the amount of external feedback as connection weights. The predictions of the simple model are confirmed both with extensive numerical examples using the laser rate equations and also by experiments with GaAlAs injection lasers. The inputs and connection weights to this laser neural network are provided by external masks which control the amount of feedback reaching the laser. Stochastic learning is used to obtain weight masks for a small three-input and four-output neural net for the numerical and experimental examples. Winner-take-all and exclusive-or operations are obtained on the input set with different weight masks. Both of these operations are also obtained in experiments with a three-input/four-output laser neural network operating at an estimated speed greater than 10 GCPS. The eventual speed of this type of neural network hardware is expected to reach well within TCPS range if it is built in an optoelectronic integrated circuit with dimensions in the order of a mm. Different neural-network architectures possible with this approach are discussed.