The time frame for infants' acquisition of language constancy was probed, using the phonetic variation in a rarely heard accent (South African English) or a frequently heard accent (American English). A total of 156 Australian infants were tested. Six‐month‐olds looked longer to Australian English than less commonly heard South African accent, but at 9 months, showed similar looking times. With the more frequently heard American accent, 3‐month‐olds looked longer to Australian and American English, whereas 6‐month‐olds looked equally. Together these results imply that in the 1st year, differential attention to native versus nonnative accents decreases as infants develop a sense of language constancy for the common native language. However, experience with the nonnative accent can expedite this process.