Listening to speech is difficult in noisy environments, and is even harder when the interfering noise consists of intelligible speech as compared to non-intelligible sounds. This suggests that the ignored speech is not fully ignored, and that competing linguistic information interferes with the neural processing of target speech. We tested this hypothesis using magnetoencephalography (MEG) while participants listened to target clear speech in the presence of distracting noisevocoded signals. Crucially, the noise vocoded distractors were initially unintelligible but were perceived as intelligible speech after a small training session. We compared participants' performance in the speech-in-noise task before and after training, and neural entrainment to both target and distracting speech. The comprehension of the target clear speech was reduced in the presence of intelligible distractors as compared to when they were unintelligible. The neural entrainment to target speech in the delta range (1-4 Hz) reduced in strength in the presence of an intelligible distractor. In contrast, neural entrainment to distracting signals was not significantly modulated by intelligibility. These results support and extend previous findings, showing, first, that the masking effects of distracting speech originate from the degradation of the linguistic representation of target speech, and second, that delta entrainment reflects linguistic processing of speech.