The classification of biological samples measured by DNA microarrays has been a major topic of interest in the last decade, and several approaches to this topic have been investigated. However, till now, classifying the high-dimensional data of microarrays still presents a challenge to researchers. In this chapter, we focus on evaluating the performance of the training algorithms of the single hidden layer feedforward neural networks (SLFNs) to classify DNA microarrays. The training algorithms consist of backpropagation (BP), extreme learning machine (ELM) and regularized least squares ELM (RLS-ELM), and an effective algorithm called neural-SVD has recently been proposed. We also compare the performance of the neural network approaches with popular classifiers such as support vector machine (SVM), principle component analysis (PCA) and fisher discriminant analysis (FDA).