Spectral unmixing is an important issue to analyze remotely sensed hyperspectral data. Although the linear mixture model has obvious practical advantages, there are many situations in which it may not be appropriate and could be advantageously replaced by a nonlinear one. In this paper, we formulate a new kernel-based paradigm that relies on the assumption that the mixing mechanism can be described by a linear mixture of endmember spectra, with additive nonlinear fluctuations defined in a reproducing kernel Hilbert space. This family of models has clear interpretation, and allows to take complex interactions of endmembers into account. Extensive experiment results, with both synthetic and real images, illustrate the generality and effectiveness of this scheme compared with state-of-the-art methods.