In this paper, we investigate the relationship between the use of discourse relations and the CEFR-level of argumentative English learner essays. Using both the Rhetorical Structure Theory (RST) and the Penn Discourse TreeBank (PDTB) frameworks, we analyze essays from The International Corpus Network of Asian Learners (ICNALE), and the Corpus and Repository of Writing (CROW). Results show that the use of the RST relations of Explanation and Background, as well as the first-level PDTB sense of Contingency, are influenced by the English proficiency level of the writer.