Bilingual speakers must acquire the phonemic inventory of 2 languages and need to recognize spoken words cross-linguistically; a demanding job potentially made even more difficult due to dialectal variation, an intrinsic property of speech. The present work examines how bilinguals perceive second language (L2) accented speech and where accommodation to dialectal variation takes place. Dialectal effects were analyzed at different levels: An AXB discrimination task tapped phonetic-phonological representations, an auditory lexical-decision task tested for effects in accessing the lexicon, and an auditory priming task looked for semantic processing effects. Within that central focus, the goal was to see whether perceptual adjustment at a given level is affected by 2 main linguistic factors: bilinguals’ first language and age of acquisition of the L2. Taking advantage of the cross-linguistic situation of the Basque language, bilinguals with different first languages (Spanish or French) and ages of acquisition of Basque (simultaneous, early, or late) were tested. Our use of multiple tasks with multiple types of bilinguals demonstrates that in spite of very similar discrimination capacity, French-Basque versus Spanish-Basque simultaneous bilinguals’ performance on lexical access significantly differed. Similarly, results of the early and late groups show that the mapping of phonetic-phonological information onto lexical representations is a more demanding process that accentuates non-native processing difficulties. L1 and AoA effects were more readily overcome in semantic processing; accented variants regularly created priming effects in the different groups of bilinguals.