For decades, behavioral methods, such as the head-turning or sucking paradigms, have been the primary tools to investigate speech perception and learning of a language in infancy. Recently, however, new methods provided by event-related potentials have emerged. These are called mismatch negativity (MMN) and late discriminative negativity (LDN). MMN, the brain’s automatic change-detection response in audition, has been intensively used in adults in both basic and clinical studies for longer than 20 years. LDN, on the other hand, was only recently discovered. There seem to be many differences between these two responses. MMN is developmentally quite stable and can be obtained even from preterm infants. LDN, however, can be obtained most reliably from young children, and its amplitude decreases as a function of age. New data suggest that both of these responses have a special role in language processing, although both of them can also be elicited by nonspeech stimuli.