The softening process observed in the steep decay phase of early X-ray afterglows of Swift bursts has remained a puzzle since its discovery. The softening process can also be observed in the later phase of the bursts and its cause has also been unkno
wn. Recently, it was suggested that, influenced by the curvature effect, emission from high latitudes would shift the Band function spectrum from higher energy band to lower band, and this would give rise to the observed softening process accompanied by a steep decay of the flux density. The curvature effect scenario predicts that the terminating time of the softening process would be correlated with the duration of the process. In this paper, based on the data from the UNLV GRB group web-site, we found an obvious correlation between the two quantities. In addition, we found that the softening process can be divided into two classes: the early type softening ($t_{s,max}leq 4000s$) and the late type softening ($t_{s,max} > 4000s$). The two types of softening show different behaviors in the duration vs. terminating time plot. In the relation between the variation rates of the flux density and spectral index during the softening process, a discrepancy between the two types of softening is also observed. According to their time scales and the discrepancy between them, we propose that the two types are of different origins: the early type is of internal shock origin and the late type is of external shock origin. The early softening is referred to the steep decay just following the prompt emission, whereas the late decay typically conceives the transition from flat decay to late afterglow decay. We suspect that there might be a great difference of the Lorentz factor in two classes which is responsible for the observed discrepancy.
