Efficient comprehension of sentences requires rapidly and continuously accessing and integrating different sources of information in real time. Psycholinguists have developed detailed models and theories to account for the processes involved in on-line sentence comprehension as well as a number of sophisticated experimental designs for studying these processes. But how about real-time sentence processing in bilinguals? The study of bilingual sentence processing has received considerable attention and has led to a remarkable growth of experimental studies over the last 10 years. The focus of these studies has been on late bilinguals, i.e., on second-language (L2) learners who learned a non-native language after early childhood, as adolescents or adults. These studies have revealed both similarities and differences between native (L1) and non-native (L2) sentence processing. Several proposals have been made to account for the experimental findings, but the significance and nature of native vs. non-native differences in sentence processing has remained controversial. Some researchers have claimed that L1 and L2 sentence processing are essentially the same and that observed performance differences between native and non-native sentence comprehension are due to peripheral factors, e.g., decoding problems, working memory limitations, slower processing speed, difficulties with lexical access and retrieval, or a reduced ability to predict during L2 processing (e.g., McDonald, 2006; Hopp, 2016; Kaan, 2014). Others have posited more substantial differences between L1 and L2 processing. One prominent proposal is Clahsen and Felser's (2006a, b) Shallow-Structure Hypothesis (SSH). Assuming multi-stream models of language processing (e.g., Ferreira & Patson, 2007) with two routes from form to meaning, a heuristic one that employs surface-form information, lexical and semantic cues, and an algorithmic route that relies on a full grammatical parse, the SSH holds that L2 processing relies less on grammatical and more on non-grammatical information sources, in comparison to L1 processing of syntactic (and morphological) phenomena.