Wavelet Neural Networks (WNNs) are complex artificial neural systems and their training can be a challenge. In the past, most common training schemes for WNNs, such as gradient descent, have been restricted to training only a subset of differentiable parameters. In this paper, we propose an evolutionary method to train both differentiable and non-differentiable parameters using the concept of Cartesian Genetic Programming (CGP). The approach was evaluated on the two-spiral task and on real-world datasets for the detection of breast cancer and Parkinson’s disease. In our experiments, the performance of the proposed method was comparable to several standard methods of classification. On the breast cancer dataset, the performance was better than other non-ensemble and multistep processing methods. The experimental results show how the performance of WNNs depends on the number of wavelons used. The presented case studies demonstrate that the proposed WNNs perform competitively in comparison to several other methods and results reported in literature.