Recent ERP data from young adults have revealed that simple syntactic anomalies elicit different patterns of lateralization in right‐handed participants depending upon their familial sinistrality profile (whether or not they have left‐handed biological relatives). Right‐handed participants who do not have left‐handed relatives showed a strongly lateralized response pattern, with P600 responses following left‐hemisphere‐biased presentations and N400 responses following right‐hemisphere‐biased presentations. Given that the literature on aging has documented a tendency to change across adulthood from asymmetry of function to a more bilateral pattern, we tested the stability of this asymmetric response to syntactic violations by recording ERPs as 24 older adults (age 60+) with no history of familial sinistrality made grammaticality judgments on simple two‐word phrases. Results showed that the asymmetric pattern observed in right‐handed adults without familial sinistrality indeed changes with age, such that P600 responses come to be elicited not only with left‐hemisphere‐biased but also with right‐hemisphere‐biased presentations in older adults. These findings suggest that, as with many other cognitive functions, syntactic processing becomes more bilateral with age.