Paying attention to one speaker in noisy environments can be extremely difficult. This is because task-irrelevant speech competes for processing resources with attended speech. However, whether this competition is restricted to acoustic-phonetic interference, or if it extends to competition for linguistic processing as well, remains highly debated. To address this debate, here we test whether task-irrelevant speech sounds are integrated over time to form hierarchical representations of lexical and syntactic structures.Neural activity was recorded using Magnetoencephalography (MEG) during a dichotic listening task, where human participants attended to natural speech presented to one ear, and task-irrelevant stimuli were presented to the other. Task-irrelevant stimuli consisted either of random sequences of syllables (Non-Structured), or syllables ordered to form coherent sentences (Structured). Using hierarchical frequency-tagging, the neural signature of different linguistic-hierarchies within the Structured stimuli – namely words, phrases and sentences – can be uniquely discerned from the neural response.We find that, indeed, the phrasal structure of task-irrelevant stimuli was represented in the neural response, primarily in left inferior frontal and posterior parietal regions. Moreover, neural tracking of attended speech in left inferior frontal regions was enhanced when task-irrelevant stimuli were linguistically structured. This pattern suggests that syntactic structurebuilding processes are applied to task-irrelevant speech, at least under these circumstances, and that selective attention does not fully eliminate linguistic processing of task-irrelevant speech. Rather, the inherent competition for linguistic processing resources between the two streams likely results in the increased listening effort experienced when trying to focus selective attention in multi-speaker contexts.Significance statementThis study addresses the fundamental question of how the brain deals with competing speech in noisy environments. Specifically, we ask: when one attempts to focus their attention on a particular speaker, what level of linguistic processing is applied to other, task-irrelevant speech? By measuring neural activity, we find evidence that the phrasal structure of task-irrelevant speech is indeed discerned, indicating that linguistic information is integrated over time and undergoes some syntactic analysis. Moreover, neural responses to attended speech were also enhanced in speech-processing regions, when presented together with comprehensible yet task-irrelevant speech. These results nicely demonstrate the inherent competition for linguistic processing resources among concurrent speech, providing evidence that selective attention does not fully eliminate linguistic processing of task-irrelevant speech.