Plastic changes of saccades (i.e. following saccadic adaptation) do not transfer between oppositely-directed saccades except when multiple directions are simultaneously trained, suggesting a saccadic planning in retinotopic coordinates. Interestingly, a recent study in human healthy subjects revealed that after an adaptive increase of rightward scanning saccades, both leftward and rightward double-step memory-guided saccades triggered toward the adapted endpoint were modified, revealing that target location was coded in spatial coordinates (Zimmerman et al., 2011). However, as the computer screen provided a visual frame, one alternative hypothesis could be a coding in allocentric coordinates. Here, we questioned whether adaptive modifications of saccadic planning occur in multiple coordinate systems. We reproduced Zimmerman's paradigm using target LEDs in the dark with and without a visual frame, and tested different saccades before and after adaptation. With double-step memory-guided saccades, we reproduced the transfer of adaptation to leftward saccades with the visual frame but not without, suggesting that the coordinate system used for saccade planning when the frame is visible is allocentric rather than spatiotopic. With single-step memory-guided saccades, adaptation transferred to leftward saccades both with and without the visual frame, revealing a target localization in a coordinate system, which is neither retinotopic nor allocentric. Finally, with single-step visually-guided saccades, the classical unidirectional pattern of amplitude change was reproduced, revealing a retinotopic coordinates coding. These experiments indicate that the same procedure of adaptation modifies saccadic planning in multiple coordinate systems in parallel, each of them being revealed by the use of different saccade tasks in post-adaptation.