While a common approach to address nonlinear distortions, emitted by multiple loudspeakers and observed by multiple microphones, is to use post-filtering techniques, this paper proposes a cooperative strategy to rather model and then cancel such distortions. In this approach, the overall problem of modeling distortions emitted by a number of loudspeakers is divided into multiple simpler and easier tasks of estimating distortions emitted by subsets of loudspeakers. This approach allows also the exploitation of the physical configuration of the loudspeakers and microphones to select certain microphone signals for estimating the nonlinearity of loudspeakers that contribute the predominant part of the acoustic echo to this microphone signal. The proposed strategy is realized using the elitist resampling particle filter and the Gaussian particle filter. Both variants are evaluated and compared to a linear approach using synthesized and real recordings.