Recently, the transient characteristics of postural sway have been suggested as an alternative or an improvement to traditional whole-trial analyses, possibly reflecting the sensory reweighing process. The purpose of this study was to assess if the transient characteristics of postural sway are sensitive to age and postural tasks. Twenty young adults (18–27 years old) and fifteen older adults (67–80 years old) performed parallel (eyes open and eyes closed), tandem and single-leg postural tasks for 30 s. Centre of pressure (CoP) velocity, amplitude and frequency were derived from force plate data. In addition to whole-trial estimates, we calculated the relative differences between the 1st and the 2nd (DIF_21) and the 1st and the 3rd (DIF_31) 10 s time intervals. Postural sway increased with the difficulty of the task, and the increase was more pronounced in the older adult group (p < 0.001; η2 = 0.31–0.38 for group × task interactions). Large and statistically significant age × task interactions were shown for both DIF_21 and DIF_31 for CoP anterior–posterior frequency (p < 0.001; η2 = 0.17–0.18). Possible age differences were also indicated for the transient response in CoP medial–lateral velocity in the parallel stance task. Specifically, we found an exaggerated transient response (i.e., relatively higher COP velocity in the first 10 s) in older adults compared to young adults when visual information was restored during the parallel quiet stance. This study shows the potential for an application of measures of the transient behavior of postural sway after the removal or restoration of visual information.