This research focuses on investigating the writing potential of non-English speaking background (NESB) undergraduate students in construing PERIODICITY (Martin and Rose, 2007). PERIODICITY allows the study of the organization of information waves in texts. In this research, the construal of PERIODICITY is evident from the higher-level Themes and News (i.e. macroTheme, macroNew, hyperTheme and hyperNew) that develop hierarchical delivery of meanings. A Taxonomy of Entities is proposed to examine the use of different kinds of entities (including grammatical metaphor) in the layers of information waves. The shift in meaning potential in the students' texts is described using Commitment Theory. The data used in this study consists of the texts produced by NESB students from an English medium university in Hong Kong, who participated in both the Language Companion Course (LCC) and the Scaffolding Literacy in Adult and Tertiary Environments (SLATE) projects aimed to enhance students' writing proficiency. The data was gathered over three consecutive semesters, with the first semester profiling the students' texts without any assigned language support, and the subsequent two semesters including two assignments of the same genre and two drafts of each assignment having had LCC-and-SLATE intervention. This allows both ontogenetic (between assignments) and logogenetic (between drafts) study of the students' texts with the same genre. The students demonstrated both logogenetic and ontogenetic improvement in PERIODICITY across the three semesters, especially on the construal of higherhierarchical information wave (i.e. macroTheme and macroNew). However, only limited improvement was observed in the use of entities to preview and accumulate ideas in the text. These findings should be usefully applied for enriching students' linguistic resources for construing better periodic structure in their writing.