A simple parametric model is proposed for data from a point-process version of a reaction time experiment. It is used to statistically check for the presence and nature of nonlinear inhibition in the eye-brain-hand system, as well as to study the nature of the reaction time delay distribution. The model tells us that, in principle, the second-order intensity estimate can be used to determine whether the experimental subject is systematically observing the first or the second of two flashes transmitted in short succession. Nonparametric estimates of second-order intensity functions are used in conjunction with this model. In particular, the model allows for the computation of good bandwidths for intensity curve estimation. A parametric bootstrap can also be implemented. Our methods are illustrated with 12 runs of data from a real reaction time experiment. It is found that nonlinear inhibition is present in the eye-brain-hand system. However, there are insufficient data to distinguish between log-normality and normality in the reaction time distribution, due partly to confounding with the particular kind of nonlinear inhibition present in the system.