Saccadic oscillations are unwanted back-to-back saccades occurring one upon the other that produce a high-frequency oscillation of the eyes (usually 15-30 Hz). These may occur transiently in normal subjects, for example, around the orthogonal axis of a purely horizontal or vertical saccade, during combined saccade-vergence gaze shifts or during blinks. Some subjects may produce saccadic oscillations at will, usually with convergence. Pathological, involuntary saccadic oscillations such as flutter and opsoclonus are prominent in certain diseases. Our recent mathematical model of the premotor circuit for generating saccades includes brainstem burst neurons in the paramedian pontine reticular formation (PPRF), which show the physiological phenomenon of post-inhibitory rebound (PIR). This model makes saccadic oscillations because of the positive feedback among excitatory and inhibitory burst neurons. Here we review our recent findings and hypotheses and show how they may be reproduced using our lumped model of the saccadic premotor circuitry by reducing the inhibitory efficacy of omnipause neurons.