Two languages, historically related, both have lexical stress, with word stress distinctions signalled in each by the same suprasegmental cues. In each language, words can overlap segmentally but differ in placement of primary versus secondary stress (OCtopus, ocTOber). However, secondary stress occurs more often in the words of one language, Dutch, than in the other, English, and largely because of this, Dutch listeners find it helpful to use suprasegmental stress cues when recognising spoken words. English listeners, in contrast, do not; indeed, Dutch listeners can outdo English listeners in correctly identifying the source words of English word fragments (oc-). Here we show that Dutch-native listeners who reside in an English-speaking environment and have become dominant in English, though still maintaining their use of these stress cues in their L1, ignore the same cues in their L2 English, performing as poorly in the fragment identification task as the L1 English do.