We derive a new method for solving nonlinear blind source separation problems by exploiting second-order statistics in a kernel induced feature space. This paper extends a new and efficient closed-form linear algorithm to the non-linear domain using `the kernel trick' originally applied in Support Vector Machines. This technique could likewise be applied to other linear covariance-based source separation algorithms. Experiments on realistic nonlinear mixtures of speech signals, gas multisensor data and visual disparity data illustrate the applicability of our approach.