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Nuisance attribute projection (NAP) was successfully applied in SVM-based speaker verification systems to improve performance by doing projection to remove dimensions from the SVM feature space that cause unwanted variability in the kernel. Previous studies of NAP were focused mainly on linear and generalized linear kernel SVMs. In this paper, NAP in nonlinear kernel SVMs, e.g. polynomial or Gaussian kernels, are investigated. Instead of doing explicit feature expansion and projection in high-dimension feature space, kernel principal component analysis is employed to find nuisance dimensions; and, NAP is carried out implicitly by incorporating it into some compensated kernel functions. Experimental results on the 2006 NIST SRE corpus indicate the effectiveness of such nonlinear kernel NAP. Compared with linear NAP, nonlinear NAP with Gaussian kernel obtained about 11% relative improvement in equal error rate (EER).