The incidence of nativelikeness in adult second language acquisition is a controversial issue in SLA research. Although some researchers claim that any learner, regardless of age of acquisition, can attain nativelike levels of second language (L2) proficiency, others hold that attainment of nativelike proficiency is, in principle, impossible. The discussion has traditionally been framed within the paradigm of a critical period for language acquisition and guided by the question of whether SLA is constrained by the maturation of the brain. The work presented in this article can be positioned among those studies that have focused exclusively on the apparent counterexamples to the critical period. We report on a large-scale study of Spanish/Swedish bilinguals (n = 195) with differing ages of onset of acquisition (<1–47 years), all of whom identify themselves as potentially nativelike in their L2. Listening sessions with native-speaker judges showed that only a small minority of those bilinguals who had started their L2 acquisition after age 12, but a majority of those with an age of onset below this age, were actually perceived as native speakers of Swedish. However, when a subset (n = 41) of those participants who did pass for native speakers was scrutinized in linguistic detail with a battery of 10 highly complex, cognitively demanding tasks and detailed measurements of linguistic performance, representation, and processing, none of the late learners performed within the native-speaker range; in fact, the results revealed also that only a few of the early learners exhibited actual nativelike competence and behavior on all measures of L2 proficiency that were employed. Our primary interpretation of the results is that nativelike ultimate attainment of a second language is, in principle, never attained by adult learners and, furthermore, is much less common among child learners than has previously been assumed.