Amyotrophic lateral sclerosis (ALS) is a mortal and idiopathic neurodegenerative disturbance of the human motor system. The disturbances of locomotion due to neurodegenerative diseases (NDDs) consisting of ALS, Parkinson disease (PD), and Huntington disease (HD) cause some abnormal fluctuations in gait signals. The investigation into gait patterns of NDDs provides significant information in order to develop new biomedical diagnosis devices. The main objective of this study is to evaluate the best discrimination method of ALS among control subjects (Co.), PD patients, and HD patients. The D2, D4, D5, and D6 detailed components, which were determined as critical features extracted from gait signals using discrete wavelet transform analysis in our previous study, are used as the inputs of all classification methods of the present study. Multilayer perceptron neural networks (MLPNNs), radial basis function neural networks, generalized regression neural networks, support vector machines, and decision tree classifiers are evaluated in this study. The MLPNN classifier, for which the average accuracy percentage is calculated as 92.09{\%}, is evaluated as the most accomplished method. The best leave-one-out cross-validation (LOOCV) score as testing{\%} (all-training-all-testing{\%}) in MLPNN is calculated as 96.55{\%} (99.76{\%}) for ALS vs. Co. discrimination. Other LOOCV scores with MLPNNs are calculated as 82.14{\%} (99.36{\%}) for ALS vs. PD, 78.79{\%} (99.17{\%}) for ALS vs. HD, 83.33{\%} (98.87{\%}) for ALS vs. HD+PD, and 82.81{\%} (99.00{\%}) for ALS vs. HD+PD+Co., respectively. Consequently, this study proposes a new classification method based on MLPNNs to discriminate ALS among other NDDs and Co. after comparing the results.