Measures of eye movement dysfunction have been considered as candidate endophenotypes for the study of genetic liability in schizophrenia. In this respect it is crucial to confirm a clinical state independentce of these measures. Twenty people with DSM-IV schizophrenia were assessed using a battery of oculomotor tasks in the acute phase of their disorder without being treated with antipsychotic medication and then again in the remission phase under treatment with antipsychotic medication. The saccade latency in the saccade task, the error rate and antisaccade latency in the antisaccade task, and the frequency of unwanted saccades in the active fixation task were stable in time both at the group level and within each individual, showing no relation to the significant improvement in different psychopathological dimensions of these patients. The root mean square error, gain and saccade frequency in the pursuit task were not stable over time, although again this instability was not related to the changes in psychopathological status of these patients. Finally, the saccade frequency in the active fixation task with distracters was not stable in time and was correlated with changes in specific dimensions of psychopathology. These results provide further evidence that saccade and smooth eye pursuit dysfunction measures are not affected by the substantial change in the clinical state of schizophrenia from the acute phase to remission, and strengthen the current view that they can be used as endophenotypes. On the other hand, active fixation might be state-dependent adding to the evidence against its use as a candidate endophenotype in schizophrenia.