How native-like is non-native language processing?

Following several decades of research on native language (L1) processing, psycholinguists have more recently begun to investigate how non-native language (L2) speakers comprehend and process language in real time. Regarding the traditional assumption that L2 learners have 'difficulty with grammar', this new research has revealed some unexpected similarities and differences between L1 and L2 processing. Specifically, it appears that L2 processing can become native-like in some linguistic subdomains (including certain aspects of grammar) but that L1 and L2 processing differences persist in the domain of complex syntax, even in highly proficient L2 speakers. Thus, more subtle linguistic distinctions seem to be required to understand the nature of non-native language processing.