Sensorimotor adaptation restores and maintains the accuracy of goal-directed movements. It remains unclear whether these adaptive mechanisms modify actions by controlling peripheral premotor stages that send commands to the effectors and/or earlier processing stages involved in registration of target location. Here, we studied the effect of adaptation of saccadic eye movements, a well-established model of sensorimotor adaptation, in an antisaccade task. This task introduces a clear spatial dissociation between the actual target direction and the requested saccade direction because the correct movement direction is in the opposite direction from the target location. We used this requirement of a vector inversion to assess the level(s) of saccadic adaptation for two different types of adapted saccades. In two different experiments, we tested the transfer to antisaccades of the adaptation in one direction of reactive saccades to jumping targets and of scanning voluntary saccades within a target array. In the first experiment, we found that adaptation of reactive saccades transferred only to antisaccades in the adapted direction. In contrast, in the second experiment, adaptation of scanning voluntary saccades transferred to antisaccades in both the adapted and non-adapted directions. We conclude that adaptation of reactive saccades acts only downstream of the vector inversion required in the antisaccade task, whereas adaptation of voluntary saccades has a distributed influence, acting both upstream and downstream of vector inversion.