Delaminations can significantly compromise the structural integrity of composite structures. The delaminated regions are prone to sublaminate buckling, which in turn can promote the delamination growth and reduce the load carrying capacity of the structure. In this study insights into the growth characteristics of delaminations under compressive fatigue loading have been presented. The growth is considered unstable when the delamination grows abruptly to a larger size, whereas it is deemed stable when the growth occurs gradually with the load cycles. In the existing literature, growth characteristics have been studied under quasi-static loading conditions, as demonstrated in the foundational work in literature from 1980s [1]. However, the characteristics of fatigue growth have remained largely unexplored until now. The present study examines the growth behaviour in composite laminates with through-width delaminations using an analytical framework. The established model from literature [2] employs the Rayleigh-Ritz method to approximate buckling displacements and applies a quasi-brittle Griffith fracture criterion based on the energy release rate, G. The trend of G has been observed as a function of delamination size for various applied strains. Through this analysis, the maximum allowable strain for which delamination growth is expected to remain in a stable regime has been determined and also insight is drawn into the anticipated growth rate of delamination as a function of its size. Similarly, various growth conditions have been presented for quasi-static loading scenario and it has been observed that the minimum failure strain in this case correlates with the maximum allowable strain for stable growth in the fatigue scenario. By providing these insights into growth behaviour,. this study lays the foundation for incorporating the concept of slow-growth damage tolerance for the problem of delamination buckling.