Melanocytic lesions may occur in various areas of the skin and may eventually develop into malignant tissue types as a result of abnormal tissue growth. Although the gold standard for the diagnosis of melanoma is still a histopathological examination, dermatologists often use dermoscopic examination in their routine practice to reduce unnecessary excisions or to prevent misdiagnosis of clinically suspected melanocytic lesions. However, dermoscopic examinations may require special training and experience. Furthermore, even among experts, different evaluation results may occur. For these reasons, image processing and artificial intelligence application studies are performed on dermoscopic images based on information technologies developed in recent years. This study investigated the automatic classification of superficial spreading melanoma and nevocellular nevus using support vector machines. A publicly available and histopathologically verified MED-NODE data set (70 superficial spreading melanomas and 100 nevocellular naevi) was used. For the classification task, first, the energy distributions (power spectral densities) of each image in the spectral domain were obtained. Second, gray-level co-occurrence matrices were created, and the textural features of the matrices were extracted. Finally, the learning model was developed with these features as input for classification. Support vector machines were trained using validation methods, including holdout validation and stratified cross-validation. The hyperparameters were optimized using the regularization factor of 10, the radial basis kernel function, and the gamma factor of 0.0098. Using 10-fold cross-validation, we achieved a mean accuracy of 98.9% (+/- 0.01 standard deviation), 99.4% sensitivity, and 97.5% specificity.