Dynamic random-dot stimuli have been widely used to explore central mechanisms of motion processing. We have measured the responses of neurons in area MT of the alert monkey while we varied the strength and direction of the motion signal in such displays. The strength of motion is controlled by the proportion of spatiotemporally correlated dots, which we term the correlation of the stimulus. For many MT cells, responses varied approximately linearly with stimulus correlation. When they occurred, nonlinearities were equally likely to be either positively or negatively accelerated. We also explored the relationship between response magnitude and response variance for these cells and found, in general agreement with other investigators, that this relationship conforms to a power law with an exponent slightly greater than 1. The variance of the cells' discharge is little influenced by the trial-to-trial fluctuations inherent in our stochastic display, and is therefore likely to be of neural origin. Linear responses to these stochastic motion stimuli are predicted by simple, low-level motion models incorporating sensors having relatively broad spatial and temporal frequency tuning.