A neural network model based on the anatomy and physiology of the matrix compartment of the striatum is described. The model consists of a network of neurons which are mutually inhibitory within a defined domain. A membrane potassium conductance (GK) under dopaminergic-cholinergic control is included in the model. Computer simulation results show that changes in GmaxK can modulate the behaviour of the network to produce either competition or coactivation among striatal output neurons. An analysis of a two-neuron system based on the model shows that the maximum steepness of the threshold function plays a decisive role in the dynamics, in particular with regard to the competition that exists between the neurons. Competitive interactions predominate at low GmaxK, while coactivation predominates at high GmaxK. We suggest that the former dynamic governs reciprocal inhibition of antagonistic muscles, while the latter governs cocontraction and rigidity. The model offers insights into the control of striatal neurodynamics by GmaxK which establish closer links between dopaminergic actions in the striatum and the mechanism of Parkinsonian rigidity. A prediction of the model is that acetylcholine should increase GKmax in striatal output neurons.