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In this contribution, we present a variational Bayesian framework for the acoustic echo cancellation problem in the presence of a memoryless loudspeaker nonlinearity. We pursue a cascade modeling strategy, where first-order Markov models are described over the acoustic echo path and the nonlinear expansion coefficients. An iterative algorithm is then derived that learns the posterior on the echo path and the nonlinear coefficients to fit the evidence distribution. We show that the formulated variational Bayesian state-space frequency-domain adaptive filter is efficiently implementable and performs joint learning of the echo path and the loudspeaker nonlinearity. The algorithm exploits the internal exchange of the reliability information, resulting in effective linear and nonlinear echo cancellation.