We report two experiments that investigate the effects of sentence context on bilingual lexical access in Spanish and English. Highly proficient Spanish-English bilinguals read sentences in Spanish and English that included a marked word to be named. The word was either a cognate with similar orthography and/or phonology in the two languages, or a matched non-cognate control. Sentences appeared in one language alone (i.e., Spanish or English) and target words were not predictable on the basis of the preceding semantic context. In Experiment 1, we mixed the language of the sentence within a block such that sentences appeared in an alternating run in Spanish or in English. These conditions partly resemble normally occurring inter-sentential code-switching. In these mixed language sequences, cognates were named faster than non-cognates in both languages. There were no effects of switching the language of the sentence. In Experiment 2, with Spanish-English bilinguals matched closely to those who participated in the first experiment, we blocked the language of the sentences to encourage language-specific processes. The results were virtually identical to those of the mixed language experiment. In both cases, target cognates were named faster than non-cognates, and the magnitude of the effect did not change according to the broader context. Taken together, the results support the predictions of the Bilingual Interactive Activation + Model (Dijkstra & Van Heuven, 2002) in demonstrating that bilingual lexical access is language nonselective even under conditions in which language-specific cues should enable selective processing. They also demonstrate that, in contrast to lexical switching from one language to the other, inter-sentential code-switching of the sort in which bilinguals frequently engage, imposes no significant costs to lexical processing.