This dissertation investigates the frequency, semantic, and functional characteristics of recurring discontinuous formulaic language in a learner corpus of argumentative and literary essays. Discontinuous sequences of words, or ‘frames’, are recurrent sequences of words that have one or more variable slots. For example, in the * of and it is * to, where the asterisks represent variable slots in the sequences of words. A corpus of English argumentative essays authored by native speakers of English, Japanese, and Spanish is analyzed using modern methods in corpus linguistics to determine which frames are used frequently. Frequent frames are compared between the L1 groups to investigate trends in structure, frequency, and variability.\nThe focus of analysis then narrows to a group of 30 recurring frames comprised of only function words, that is, function word frames such as in the * of, the * of the, and to the * that. The 30 frames are grouped based on structural characteristics, such as noun and preposition-based frames, for further analysis to better understand their semantic and functional characteristics. A lexical database is used to explore the semantic characteristics of fillers of the frames. To determine discourse functions of all instances of each of the 30 target frames, a well-known taxonomy previously applied to continuous sequences of words is adapted and applied to the present context. Discourse functions of the frames are then used as dependent variables in a multinomial logistic regression conducted with four distinct predictor variables: (1) L1, (2) proficiency level, (3) topic of essay, and (4) specific frame. The purpose of the regression is to see which predictor best accounts for discourse function fulfilled by frames from the structural groups.\nFindings from the various analyses first indicate that Japanese learners of English use function word frames at far lower rates than the L1 English and Spanish speakers. Secondly, fillers of the structural groups of function word frames tend to be abstract nouns and the frames largely serve the discourse function of intangible framing of a following noun phrase. In terms of predictor variables, the frames themselves, particularly prepositions, best predict discourse function. The results lend support to the idea that function words, despite carrying little meaning in isolation, are semantically motivated and systematically contribute meaning to larger sequences of words. Pedagogical implications of this study include the teaching of function words from a more phraseological perspective as well as highlighting the connection between frames, fillers, and discourse functions.