We describe the responses during and after motion of slow cells, which are a class of direction-selective neurons in the pretectal nucleus of the optic tract (NOT) of the wallaby. Neurons in the NOT respond to optic flow generated by head movements and drive compensatory optokinetic eye movements. Motion in the preferred direction produces increased firing rates in the cells, whereas motion in the opposite direction inhibits their high spontaneous activities. Neurons were stimulated with moving spatial sinusoidal gratings through a range of temporal and spatial frequencies. The slow cells were maximally stimulated at temporal frequencies <1 Hz and spatial frequencies of 0.13-1 cpd. During motion, the responses oscillate at the fundamental temporal frequency of the grating but not at higher-order harmonics. There is prolonged excitation after preferred direction motion and prolonged inhibition after anti-preferred direction motion, which are referred to as same-sign after-responses (SSARs). This is the first time that the response properties of neurons with SSARs have been reported and modeled in detail for neurons in the NOT. Slow cell responses during and after motion are modeled using an array of Reichardt-type motion detectors that include band-pass temporal prefilters. The oscillatory behavior during motion and the SSARs can be simulated accurately with the model by manipulating time constants associated with temporal filtering in the prefilters and motion detectors. The SSARs of slow cells are compared with those of previously described direction-selective neurons, which usually show transient inhibition or excitation after preferred or anti-preferred direction motion, respectively. Possible functional roles for slow cells are discussed in the context of eye movement control.