The literature on the topical organization of essays suggests that there are four possible types of progression from the topic of one clause to the topics of the following clauses. These are parallel, sequential, extended parallel, and extended sequential progressions. Essay writers' ability to create cohesion and coherence can be evaluated on the extent of their capability to use topical progression appropriately and adequately. In other words, essays in which topical structuring is properly accomplished are more cohesive and coherent. Based on this fact, this study aims to analyze the topical structure in argumentative essays written by Turkish learners of EFL. Our objectives in doing this are (1) to assess Turkish EFL learners' ability to construct topical links between clauses, (2) to identify the type of progression mostly preferred by them, and (3) to find out the range of linguistic structures that they use to create progression. To this end, the researchers have conducted Topical Structure Analysis (TSA) on essays produced by 81 ELT students from three different universities in Turkey (Gaziantep, Inönü, and Hakkari). The analysis illustrated the fact that Turkish EFL learners are not as skilled as they should be in topical structuring. It also revealed that they usually prefer to use parallel and sequential types of progression, while extended progression has been observed to be less common in their essays. Finally, we found that the participants of the study mostly use pronouns for parallel progression, whereas they switch to new noun phrases for sequential progression.