Standing and walking are very different tasks. It might be reasonable, therefore, to assume that the mechanisms used to maintain the stability of standing and walking should be quite different. However, many studies have shown that postural stability measures can generally predict risk of falls, even though most falls occur during locomotor tasks and not during postural tasks. This suggests that there is at least some commonality among the mechanisms governing the control of both standing and walking. The present study was conducted to determine whether the postural stability either is or is not directly related to locomotor stability. Twenty healthy adults, age 18–73 years, walked on a motorized treadmill at their preferred walking speed for three trials of 5 min. They also stood on a force plate for three trials of 5 min. Both tasks were performed without imposing any additional external perturbations. The motion of each subject’s trunk segment was recorded and described using a multi-dimensional state space defined in the same manner for both tasks. Local dynamic stability was quantified from the mean divergence over time of locally perturbed trajectories in state space, which was parameterized as a double exponential process. Divergence parameters were compared to determine the relationship between local dynamic stability during standing and walking. Standing and walking exhibited local dynamic stability properties that were significantly different (P<​0.001) and not correlated (P>​0.1). Divergence parameters were also compared to traditional center of pressure (COP) measures obtained from standing trials. COP measures were significantly correlated to local divergence parameters for standing, but not to those for walking. This study provides direct evidence that the mechanisms governing standing and walking stability are significantly different.