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Retrieving unknown sources from nonlinear mixtures of them requires one to define a separating structure, before proceeding to methods for estimating mixing or separating parameters in blind configurations. Recurrent neural networks are attractive separating structures for a wide range of nonlinear mixing models. In a previous paper, we proposed such a network for the non-blind version of linear-quadratic separation. We here extend this approach to the more difficult blind case. We optimize the fixed points and stability of this structure thanks to its free weights. We define the general architecture of future adaptation algorithms that will be able to take advantage of these free weights. Numerical results illustrate the theoretical properties derived in this paper.