We present a neural model of the frontal eye fields. It consists of several retinotopic arrays of neuron-like units that are recurrently connected. The network is trained to make memory-guided saccades to sequentially flashed targets that appear at arbitrary locations. This task is interesting because the large number of possible sequences does not permit a pre-learned response. Instead locations and their priority must be maintained in active working memory. The network learns to perform the task. Surprisingly, after training it can also select targets in visual search tasks. When targets are shown in parallel it chooses them according to their salience. Its search behavior is comparable to that of humans. It exhibits saccadic averaging, increased reaction times with more distractors, latency vs accuracy trade-offs, and inhibition of return. Analysis of the network shows that it operates like a queue, storing the potential targets in sequence for later execution. A small number of unit types are sufficient to encode this information, but the manner of coding is non-obvious. Units respond to multiple targets similar to quasi-visual cells recently studied [Exp. Brain Res. 130 (2000) 433]. Predictions are made that can be experimentally tested.