Asymmetry in cortical activity was tested for short‐ and long‐term stability during the first year of life. Infants (N = 129) completed a total of four laboratory visits: two visits occurred about 1 week apart when infants were 6 months old, and two visits occurred about 1 week apart when infants were 12 months of age. At each laboratory visit, EEG readings were taken during five 1‐min, neutral baselines as well as during a negative and a positive emotion‐eliciting task. The stability of hemispheric asymmetry was assessed at midfrontal (F3/4, F7/8) and parietal (P3/4) electrode sites. Asymmetry in baseline and fear‐eliciting episodes showed moderate short‐term stability. Long‐term stability was apparent when assessments were composited at 6 months and 12 months. Frontal asymmetry was greater than parietal asymmetry for baseline recordings. There was minimal evidence for stability in asymmetry during positive emotion tasks. Results are discussed with regard to the collection and interpretation of alpha asymmetry measures during infancy.