For tertiary level students, organising and writing texts requires a considerable amount of time. To minimize this issue, they need to be taught how to organise a text as a whole. In Systemic Functional Linguistics, the notion of periodicity can help teachers explain to students how to organise their texts successfully. As Martin and Rose (2007) state, “periodicity is concerned with information ﬂow: the way in which meanings are packaged to make it easier for us to take them in” (p. 188). The pedagogical purpose of this study is to propose the integration of the notion of periodicity when teaching writing to EFL learners at the tertiary level to improve the coherence and cohesion of their academic essays. Using central ideas from systemic functional linguistics, this study shows how coherence and cohesion were developed in two academic essays by analysing their hierarchical structures. Essay A followed a traditional composition style method and Essay B followed a suggested method using ideas from the notion of periodicity. The results showed that the hierarchical structure of Essay B was more consistent and organised than Essay A. The paper concludes with the introduction of an outline that aims to improve the quality of EFL learners’ essays in terms of their coherence and cohesion.