The electro-oculogram (EOG) is the most widely used technique for recording eye movements in clinical settings. It is inexpensive, practical, and non-invasive. Use of EOG is usually restricted to horizontal recordings as vertical EOG contains eyelid artefact (Oster & Stern, 1980) and blinks. The ability to analyse two dimensional (2D) eye movements may provide additional diagnostic information on pathologies, and further insights into the nature of brain functioning. Simultaneous recording of both horizontal and vertical EOG also introduces other difficulties into calibration of the eye movements, such as different gains in the two signals, and misalignment of electrodes producing crosstalk. These transformations of the signals create problems in relating the two dimensional EOG to actual rotations of the eyes. The application of an artificial neural network (ANN) that could map 2D recordings into 2D eye positions would overcome this problem and improve the utility of EOG. To determine whether ANNs are capable of correctly calibrating the saccadic eye movement data from 2D EOG (i.e. performing the necessary inverse transformation), the ANNs were first tested on data generated from mathematical models of saccadic eye movements. Multi-layer perceptrons (MLPs) with non-linear activation functions and trained with back propagation proved to be capable of calibrating simulated EOG data to a mean accuracy of 0.33° of visual angle (SE = 0.01). Linear perceptrons (LPs) were only nearly half as accurate. For five subjects performing a saccadic eye movement task in the upper right quadrant of the visual field, the mean accuracy provided by the MLPs was 1.07° of visual angle (SE = 0.01) for EOG data, and 0.95° of visual angle (SE = 0.03) for infrared limbus reflection (IRIS®) data. MLPs enabled calibration of 2D saccadic EOG to an accuracy not significantly different to that obtained with the infrared limbus tracking data.