The authors observed children aged 1 to 7 years without any signs of epilepsy in the anamnesis. The children were examined for headaches, memory deterioration, difficulties in the learning, some types of tics, stammering, and psychomotor disinhibition. Among them, a group of 35 children characterized by specific movements of the eye balls as was shown by estimation of oculomotor nerve functions (look anxiety, "falling look") were distinguished. EEG examinations discovered the peak-wave type complexes related to the signs of petit mal of the absence type. The conclusion is a precursor of paroxysmal conditions. It is recommended that adequate anticonvulsive therapy be initiated provided the symptom is identified together with the EEG changes.