There are a number of studies concerning difference of postural control following left or right hemisphere lesions. Few studies, however, compare the role of the right and left hemisphere in learning new postural tasks. This study aimed to address this question. Twenty patients with hemiparesis after ischemic stroke in the middle cerebral artery territory (11 with a right and 9 with a left hemispheric lesion) were investigated. All subjects were trained using two different tasks during ten training sessions. In both tasks, the subjects stood on a force platform and were taught to change the position of the center of pressure (COP) presented as a cursor on a monitor screen in front of the patient. The subjects were instructed to align the COP with the target and then move the target by shifting the COP in the indicated direction. In the "Balls" task, the position of the target (a ball) varied randomly, so the subject had to learn a general strategy of voluntary COP control. In "Bricks", the subject always had to move the target in a single direction (downward) from the top to the bottom of the screen, so that a precise postural coordination had to be learned. The number of correctly performed trials for a session was scored. The task performance and its rate were analyzed and compared with respect to the lesion lateralization between two patient groups. The voluntary control of the COP position and learning course were initially impaired in all groups of patients in both tasks. In "Balls", there were no differences between the two groups of patients. In contrast, in "Bricks", there was a greater initial deficit in patients with right hemisphere lesions, while the rate of postural learning and the final performance level did not differ between the groups. With a lower initial deficit and similar rate of learning, the maximal level of the task performance was reached earlier (on the 5th day of training) in patients with left hemisphere lesions. This group stopped improving its performance during follow-up training. The results suggest that the motor structures of the right hemisphere are more involved in the precise control of COP trajectory, but not in learning. There is no difference between hemispheres in the initial performance and learning of the general strategy of voluntary COP control. Possibly, the control of specific COP trajectory needs more sensory feedback that is associated with greater involvement of the right hemisphere. This might be a reason for the greater initial impairment of this task after lesions in the right hemisphere.