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We propose novel detection algorithms for linear modulations transmitted over nonlinear satellite channels. These algorithms are derived by using a Volterra-series expansion of the useful signal and by applying the sum-product algorithm to a suitably-designed factor graph. Being soft-input soft-output (SISO) in nature, the proposed detectors can be adopted in turbo processing without additional modifications. When compared with the optimal detection algorithm for these channels, whose complexity is exponential in the channel memory, the proposed schemes result very appealing in terms of tradeoff between performance and computational complexity. Particularly, they can approach the optimal performance with a complexity only linear in the channel memory.