We replace our earlier three-dimensional h$_a$-model of a thalamic neuron (Rose & Hindmarsh, Proc. R. Soc. Lond. B 237 289-312 (1989b)) by a seven-dimensional h$_a$-model. The stability and state diagrams for this seven-dimensional model are shown to be similar to those of the three-dimensional system with which it is compared. Two examples that illustrate how the seven-dimensional model can be related to experimental recordings are then discussed in detail. In each case we show the state and stability diagrams and the time courses of the different ionic currents during the burst response. We discuss how the various components of the state diagram could be determined experimentally. These experiments are illustrated by using our model to simulate the results of actual experiments. Finally the state and stability diagrams are transferred to a current-voltage diagram. This shows the advantage of the state diagram compared with the current-voltage diagram for representing the dynamics of the firing of a thalamic neuron.