An automated method for detecting and counting eye movements using the electrooculogram (EOG) wave form during rapid-eye-movement (REM) sleep is presented. The method is formulated as a sequential decision process with decisions based on slope and amplitude threshold criteria. Signal processing techniques such as digital filtering and smoothing are used to improve the effectiveness of the method. Validation is done by using the method on EOG data from three infants and comparing the automated count of eye movements with the visual counts of human observers. The correlation coefficient between the automated and visual count is greater than 0.9, the first-order regression coefficient close to 1.0, and the zero-order regression coefficient close to 0. We believe that this method will be useful in differentiating between the substates of REM sleep in studies of cardiorespiratory physiology.