We examined the neural correlates underlying the semantic processing of native- and nonnative-accented sentences, presented in quiet or embedded in multi-talker noise. Implementing a semantic violation paradigm, 36 English monolingual young adults listened to American-accented (native) and Chinese-accented (nonnative) English sentences with or without semantic anomalies, presented in quiet or embedded in multi-talker noise, while EEG was recorded. After hearing each sentence, participants verbally repeated the sentence, which was coded and scored as an offline comprehension accuracy measure. In line with earlier behavioral studies, the negative impact of background noise on sentence repetition accuracy was higher for nonnative-accented than for native-accented sentences. At the neural level, the N400 effect for semantic anomaly was larger for native-accented than for nonnative-accented sentences, and was also larger for sentences presented in quiet than in noise, indicating impaired lexical-semantic access when listening to nonnative-accented speech or sentences embedded in noise. No semantic N400 effect was observed for nonnative-accented sentences presented in noise. Furthermore, the frequency of neural oscillations in the alpha frequency band (an index of online cognitive listening effort) was higher when listening to sentences in noise versus in quiet, but no difference was observed across the accent conditions. Semantic anomalies presented in background noise also elicited higher theta activity, whereas processing nonnative-accented anomalies was associated with decreased theta activity. Taken together, we found that listening to nonnative accents or background noise is associated with processing challenges during online semantic access, leading to decreased comprehension accuracy. However, the underlying cognitive mechanism (e.g., associated listening efforts) might manifest differently across accented speech processing and speech in noise processing.