During goal-directed reaching, our eye and hand movements are tightly coupled in space and time, with the eye typically leading the hand. It is well known that our eyes and hand quickly correct for errors that occur during movement. However, it is unclear how corrections by the eyes and hand are coordinated, and how they are affected by feedback of the hand position. To study this, we designed a set of tasks in which participants performed online corrections during reaches to a visual target, using a robotic manipulandum. In 60% of trials, a change in movement goal was indicated by a displacement of the target, with or without distractors, or by a visual cue. Reaches were performed with either online or endpoint-only feedback of the hand position, shown as a cursor. We found that the target change evoked a corrective saccade and a rapid correction in the trajectory of the hand in all conditions. The hand always started correcting earlier than the eye. Corrections of both the hand and the eye started earliest in response to a target displacement without distractors, slightly later with distractors, and latest in response to a cue; this increase in latency was larger for the eye than for the hand. Further, the hand but not the eye corrected faster when online feedback of the hand position was available. The differential effects of task and feedback on eye and hand suggest that both effectors might update the movement goal independently.