Background: Protein remote homology detection and fold recognition are central problems in computational biology. Supervised learning algorithms based on support vector machines are currently one of the most effective methods for solving these problems. These methods are primarily used to solve binary classification problems and they have not been extensively used to solve the more general multiclass remote homology prediction and fold recognition problems. Results: We present a comprehensive evaluation of a number of methods for building SVM-based multiclass classification schemes in the context of the SCOP protein classification. These methods include schemes that directly build an SVM-based multiclass model, schemes that employ a second-level learning approach to combine the predictions generated by a set of binary SVM-based classifiers, and schemes that build and combine binary classifiers for various levels of the SCOP hierarchy beyond those defining the target classes. Conclusion: Analyzing the performance achieved by the different approaches on four different datasets we show that most of the proposed multiclass SVM-based classification approaches are quite effective in solving the remote homology prediction and fold recognition problems and that the schemes that use predictions from binary models constructed for ancestral categories within the SCOP hierarchy tend to not only lead to lower error rates but also reduce the number of errors in which a superfamily is assigned to an entirely different fold and a fold is predicted as being from a different SCOP class. Our results also show that the limited size of the training data makes it hard to learn complex second-level models, and that models of moderate complexity lead to consistently better results.