This paper explores the feature of dynamicity (a composite of temporal and local properties) in research on collaborative digital writing (CDW) in academic writing assignments. The paper traces the ways in which current research typically approaches CDW and identifies the underlying elements of current and technological inquiry in this field: components of text (the process and products of writing and learning communication), external variables, such as learning orientations and group composition, and an intermediate layer of time management that is related to organizing the assignment. The paper identifies gaps in the current understanding of the phenomenon of collaborative writing for learning and pinpoints some basic weaknesses with concepts used in this research, in particular assumptions related to the time aspect of the collaborative writing process. The prevalent view of current research, which conceptualizes writing processes as predominantly time-ordered intermediate products (texts) at several designated points within the writing assignment, overlooks the sequential dynamics of textual interaction, linearity, and "local" concept construction as influential factors in CDW assignments. Instead, this paper argues for the ideas of sequential concept construction and locally changing sources for the writer at a certain point in the writing. The insights presented in this paper can help address some of these time-related shortcomings of current research. A few selected key aspects of implementing dynamicity in studies of CDW are exemplified in a CDW assignment with information science students that the author conducted back in 2016.