The accuracy of saccadic eye movements is maintained over the long term by adaptation mechanisms which decrease or increase saccade amplitude. It is still unknown whether these opposite adaptive changes rely on common mechanisms. Here, a double-step target paradigm was used to adaptively decrease (backward second target step) or increase (forward step) the amplitude of reactive saccades in one direction only. To test which sensory-motor transformation stages are subjected to these adaptive changes, we measured their transfer to anti-saccades in which sensory and motor vectors are spatially dissociated. In the backward adaptation condition, all subjects showed a significant amplitude decrease for adapted pro-saccades and a significant transfer of adaptation to anti-saccades performed in the adapted direction but not to oppositely-directed anti-saccades elicited by a target jump in the adapted direction. In the forward adaptation condition, only 14 out of 19 subjects showed a significant amplitude increase for pro-saccades, and no significant adaptation transfer to anti-saccades was detected in either the adapted or non-adapted direction. These findings suggest that, whereas the level(s) of forward adaptation cannot be resolved, the mechanisms involved in backward adaptation of reactive saccades take place at a sensory-motor level downstream from the vector inversion process of anti-saccades and differ markedly from those involved in forward adaptation.