The purpose of this study was to explore possible cerebral asymmetries in the processing of decomposable and nondecomposable idioms by fluent nonnative speakers of English. In the study, native language (Polish) and foreign language (English) decomposable and nondecomposable idioms were embedded in ambiguous (neutral) and unambiguous (biasing figurative meaning) context and presented centrally, followed by laterally presented target words related to the figurative meaning of the idiom or literal meaning of the last word of the idiom. The target appeared either immediately at sentence offset (Experiment 1), or 400 ms (Experiment 2) after sentence offset. Results are inconsistent with the Idiom Decomposition Hypothesis (Gibbs et al. in Mem Cogn 17:58–68, 1989a; J Mem Lang 28:576–593, 1989b) and only partially consistent with the idea of the differential cerebral involvement in processing (non)decomposable idioms [the Fine/Coarse Coding Theory, Beeman (Right hemisphere language comprehension: perspectives from cognitive neuroscience, Lawrence Erlbaum Associates, Mahwah, NJ, 1998)]. A number of factors, rather than compositionality per se, emerge as crucial in determining idiom processing, such as language status (native vs. nonnative), salience, or context.