In this paper, a new approach to computer supported diagnosis of skin tumors in dermatology is presented. High resolution skin surface profiles are analyzed to recognize malignant melanomas and nevocytic nevi (moles), automatically. In the first step, several types of features are extracted by 2D image analysis methods characterizing the structure of skin surface profiles: texture features based on cooccurrence matrices, Fourier features and fractal features. Then, feature selection algorithms are applied to determine suitable feature subsets for the recognition process. Feature selection is described as an optimization problem and several approaches including heuristic strategies, greedy and genetic algorithms are compared. As quality measure for feature subsets, the classification rate of the nearest neighbor classifier computed with the leaving-one-out method is used. Genetic algorithms show the best results. Finally, neural networks with error back-propagation as learning paradigm are trained using the selected feature sets. Different network topologies, learning parameters and pruning algorithms are investigated to optimize the classification performance of the neural classifiers. With the optimized recognition system a classification performance of 97.7% is achieved.