Falls while walking are frequent in patients with muscular dysfunction resulting from neurological disorders. Falls induce injuries that may lead to deconditioning and disabilities, which further increase the risk of falling. Therefore, an early gait stability index would be useful to evaluate patients in order to prevent the occurrence of future falls. Derived from chaos theory, local dynamic stability (LDS), defined by the maximal Lyapunov exponent, assesses the sensitivity of a dynamic system to small perturbations. LDS has already been used for fall risk prediction in elderly people. The aim of the present study was to provide information to facilitate future researches regarding gait stability in patients with neurological gait disorders. The main objectives were 1) to evaluate the intra-session repeatability of LDS in patients and 2) to assess the discriminative power of LDS to differentiate between healthy individuals and neurological patients. Eighty-three patients with mild to moderate neurological disorders associated with paresis of the lower extremities and 40 healthy controls participated in the study. The participants performed 2×30 s walking wearing a 3D accelerometer attached to the lower back, from which 2×35 steps were extracted. LDS was defined as the average exponential rate of divergence among trajectories in a reconstructed state-space that reflected the gait dynamics. LDS assessed along the medio-lateral axis offered the highest repeatability and discriminative power. Intra-session repeatability (intraclass correlation coefficient between the two repetitions) in the patients was 0.89 and the smallest detectable difference was 16%. LDS was substantially lower in the patients than in the controls (33% relative difference, standardized effect size 2.3). LDS measured in short over-ground walking tests seems sufficiently reliable. LDS exhibits good discriminative power to differentiate fall-prone individuals and opens up the possibility of future clinical applications for better prediction of fall risk in neurological patients.