In kernel-based machine learning algorithms, we can learn a combination of different kernel functions in order to obtain a similarity measure that better matches the underlying problem instead of using a single fixed kernel function. This approach is called multiple kernel learning (MKL). In this paper, we formulate a nonlinear MKL variant and apply it for nuclei classification in tissue microarray images of renal cell carcinoma (RCC). The proposed variant is tested on several feature representations extracted from the automatically segmented nuclei. We compare our results with single-kernel support vector machines trained on each feature representation separately and three linear MKL algorithms from the literature. We demonstrate that our variant obtains more accurate classifiers than competing algorithms for RCC detection by combining information from different feature representations nonlinearly.