In order for discourse to be considered idiomatic, it needs to exhibit features like fluency and pragmatically appropriate language use. Advances in corpus linguistics make it possible to examine idiomaticity from the perspective of recurrent word combinations. One approach to capture such word combinations is by the automatic retrieval of lexical bundles. We investigated the use of English-language lexical bundles in advanced learner writing by L1 speakers of Swedish and in comparable native-speaker writing, all produced by undergraduate university students in the discipline of linguistics. The material was culled from a new corpus of university student writing, the Stockholm University Student English Corpus (SUSEC), amounting to over one million words. The investigation involved a quantitative analysis of the use of four-word lexical bundles and a qualitative analysis of the functions they serve. The results show that the native speakers have a larger number of types of lexical bundles, which are also more varied, such as unattended "this" bundles, existential 'there' bundles, and hedging bundles. Other lexical bundles which were found to be more common and more varied in the native-speaker data involved negations. The findings are shown to be largely similar to those of the phraseological research tradition in SLA. (Contains 2 figures and 4 tables.)