Neurodegenerative diseases are one of the major concerns worldwide and have a significant impact on balance and walking ability. Gait abnormalities are indicative of early symptoms in patients with neurodegenerative diseases, even when symptoms are mild. The aim of this study is to classify neurodegenerative patients into four classes based on gait analysis using effective features derived from recurrence quantification analysis (RQA). The dataset includes gait time series data, such as stride, swing, and stance interval for both feet, from 20 Huntington's disease (HD) patients, 15 Parkinson's disease (PD) patients, 13 amyotrophic lateral sclerosis (ALS) patients, and 16 healthy controls (HC) subjects. The features extracted from RQA include recurrence rate, determinism, mean diagonal length, max line length, entropy of the diagonal line, laminarity, trap time, length of the longest vertical line, first and second recurrence times, recurrence density, clustering coefficient, and transitivity. To extract the best features, a sequential forward floating search algorithm was used, and for classification, various classical classifiers were applied. Recent studies have typically focused on binary classification, but this research also conducts a four-class classification. The four-class classification of ALS vs. PD vs. HD vs. HC using a support vector machine classifier with 4-fold cross-validation achieved an accuracy of 87.9%. Furthermore, for binary classifications, HC vs. HD, HC vs. ALS, HC vs. PD, PD vs. HD, PD vs. ALS, ALS vs. HD, and NDD vs. HC, the accuracies were 92%, 96.2%, 93.1%, 87.1%, 90.8%, 91.3%, and 91.7%, respectively. This study demonstrates the effectiveness of the RQA method and the extracted features in describing changes in nonlinear and non-stationary gait signals for assessing neurodegenerative diseases.