In the classification problem field, we often encounter many real application areas in which the data do not have an equitable distribution among the different classes of the problem. In such cases, we are dealing with the so-called imbalanced data sets. This scenario has significant interest since standard classifiers are often biased towards the majority classes, whereas the minority ones tend to have a higher reward as they usually define the concepts of interest from the learning point of view. The aim of this paper is to analyse the performance of CO²RBFN, a evolutionary cooperative–competitive model for the design of radial-basis function networks applied to classification problems on imbalanced domains, and to study its cooperation with a well-known pre-processing method, the “synthetic minority over-sampling technique”. The good performance of CO²RBFN is shown through an experimental study carried out on a large collection of imbalanced data sets where we compare, by means of a proper statistical study, the behaviour of our model with many representative neural networks algorithms, the C4.5 decision tree and a hierarchical fuzzy rule-based classification system.