This chapter presents and discusses several well-known constructive neural network algorithms suitable for constructing feedforward architectures aiming at classification tasks involving two classes. The algorithms are divided into two different groups: the ones directed by the minimization of classification errors and those based on a sequential model. In spite of the focus being on two-class classification algorithms, the chapter also briefly comments on the multiclass versions of several two-class algorithms, highlights some of the most popular constructive algorithms for regression problems and refers to several other alternative algorithms.