In this study, we explore native and non-native syntactic processing, paying special attention to the language distance factor. To this end, we compared how native speakers of Basque and highly proficient non-native speakers of Basque who are native speakers of Spanish process certain core aspects of Basque syntax. Our results suggest that differences in native versus non-native language processing strongly correlate with language distance: native/non-native processing differences obtain if a syntactic parameter of the non-native grammar diverges from the native grammar. Otherwise, non-native processing will approximate native processing as levels of proficiency increase. We focus on three syntactic parameters: (i) the head parameter, (ii) argument alignment (ergative/accusative), and (iii) verb agreement. The first two diverge in Basque and Spanish, but the third is the same in both languages. Our results reveal that native and non-native processing differs for the diverging syntactic parameters, but not for the convergent one. These findings indicate that language distance has a significant impact in non-native language processing.