The acquisition of intonation by adult learners is one of the least explored areas of second language acquisition research. The present study reports on the results of a perception experiment administered to two groups of adult learners of Spanish as an L2, with English as an L1. The first group consisted of 37 intermediate-level learners while the second group involved 18 advanced-level learners. Subjects listened to a series of 67 utterances in the L2 that varied according to the phrase accent (represented as T-), a tonal category marking the right edge of intermediate phrases in Spanish intonation. Two research questions were addressed: 1) do intermediate and advanced learners of Spanish as a second language perceive disambiguating high (H-) phrase accents in intonation contours?; and 2) employing the results of Nibert (1999, 2000) as a reference point, do these learners assign the same meanings to contours as those assigned by native Spanish listeners? The results show that: 1) both intermediate and advanced learners of Spanish attend to utterance-medial H- phrase accents in the language, 2) the advanced learners' responses to meaning approximate native-speaker judgments more closely than do the intermediate learners' responses, pointing to different stages of development, and 3) the advanced learners' responses reveal a native-like level of attainment, despite the fact that the intermediate phrasing choices interacted with syntactic structures not present in the L1, despite a lack of instruction in Spanish intonation, and despite the scarcity of positive evidence from previous input regarding the types of meaning contrasts provoked by utterance-medial H-. Within generative theory, these findings lend support to the perspective that there is full access to Universal Grammar (UG) during the L2 acquisition process.