Motion adaptation is a widespread phenomenon analogous to peripheral sensory adaptation, presumed to play a role in matching responses to prevailing current stimulus parameters and thus to maximize efficiency of motion coding. While several components of motion adaptation (contrast gain reduction, output range reduction and motion after-effect) have been described, previous work is inconclusive as to whether these are separable phenomena and whether they are locally generated. We used intracellular recordings from single horizontal system neurons in the fly to test the effect of local adaptation on the full contrast-response function for stimuli at an unadapted location. We show that contrast gain and output range reductions are primarily local phenomena and are probably associated with spatially distinct synaptic changes, while the antagonistic after-potential operates globally by transferring to previously unadapted locations. Using noise analysis and signal processing techniques to remove 'spikelets', we also characterize a previously undescribed alternating current component of adaptation that can explain several phenomena observed in earlier studies.