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Due to the fact that there exist only a small number of complex systems in artificial immune systems (AISs) that solve nonlinear problems, there is a need to develop nonlinear AIS approaches that would be among the well-known solution methods. In this study, we developed a kernel-based AIS to compensate for this deficiency by providing a nonlinear structure via transformation of distance calculations in the clonal selection models of classical AIS to kernel space. Applications of the developed system were conducted on Statlog heart disease dataset, which was taken from the University of California, Irvine Machine-Learning Repository, and on Doppler sonograms to diagnose atherosclerosis disease. The system obtained a classification accuracy of 85.93% for the Statlog heart disease dataset, while it achieved a 99.09% classification success for the Doppler dataset. With these results, our system seems to be a potential solution method, and it may be considered as a suitable method for hard nonlinear classification problems.