Textual coherence is an important part of writing. This study examines whether textual coherence affects the quality of argumentative essays by evaluating papers written by 22 EFL university students. Firstly, the argumentative essays were evaluated by two raters using an AP English Argumentative Writing rubric available on Turnitin, an online program for checking plagiarism. Then, by drawing on Danes?' (1974) Thematic Progression, the Theme and Rheme development in the essays were identified. Two essays -- one from a low-score group and one from a high-score group -- were selected as examples. The findings reveal that the low-score essays lacked a coherent thematic progression due to the frequent occurrences of brand-new Themes, and some constant Themes or Thematization of Rhemes. In contrast, the high-score essays included various patterns of thematic progression, including constant Themes, thematization of Rhemes, and several split Rhemes. The findings suggest that thematic progression, specifically with the choice and development of Themes, has influenced the coherence of whole essays, contributing to the essay scores. In addition, local cohesion strategies at a sentence level, particularly lexical cohesion, contributed to the connectivity of arguments and their supporting evidence that were expressed and realized in the forms of Themes and Rhemes. The concept of thematic progression can benefit the teaching and learning of argumentative writing in EFL contexts.