The evaluation of local divergence exponent (LDE) has been proposed as a common gait stability measure in people with multiple sclerosis (PwMS). However, differences in methods of determining LDE may lead to different results. Therefore, the purpose of the current study was to determine the effect of different sensor locations and LDE measures on the sensitivity to discriminate PwMS. To accomplish this, 86 PwMS and 30 healthy participants were instructed to complete a six-minute walk wearing inertial sensors attached to the foot, trunk and lumbar spine. Due to possible fatigue effects, the LDE short (~50% of stride) and very short (~5% of stride) were calculated for the remaining first, middle and last 30 strides. The effect of group (PwMS vs. healthy participants) and time (begin, mid, end) and the effect of Expanded Disability Status Scale (EDSS) and time were assessed with linear random intercepts models. We found that perturbations seem to be better compensated in healthy participants on a longer time scale based on trunk movements and on a shorter time scale (almost instantaneously) according to the foot kinematics. Therefore, we suggest to consider both sensor location and time scale of LDE when calculating local gait stability in PwMS.