Neurodegenerative diseases are a group of neurological conditions characterized by the loss or destruction of neurons in the central nervous system, resulting in severe impairments and death. Researchers commonly used a two-group classification (Patients with a Neurodegenerative disease vs. healthy subjects of control). Thus, the principal purpose of this article is to distinguish between Parkinson's patients and subjects with Hereditary Ataxias using machine learning techniques. We conducted experiments using a real dataset comprising Gait characteristics derived from the inertial motion sensors of a smartphone (iPhone 5S). This investigation had 67 participants, 53 of who had Parkinson's disease and 14 of whom had Hereditary Ataxias. Methods of feature selection were applied to reduce dimensionality. In addition, five classification algorithms were constructed and assessed based on their accuracy, precision, sensitivity, and specificity. The Support Vector Machine algorithm achieved an accuracy of 92.7%, a precision of 91.1%, a sensitivity of 96.2%, and a specificity of 89.1%. These results show that the suggested technique might inspire new research issues and have a direct therapeutic impact.