Perceptual systems often have to disentangle different factors from mixed observations. If each factor is represented by a set of variables, each standing for a discrete value of the factor, the factor values underlying an observation can be extracted by a winner-take-all (WTA) mechanism over the direct product of the factors. Search in the product space, however, is expensive. It is computationally attractive to work on the marginal factors. In this letter we study the dynamics of a multifactor system modeled by a number of interacting WTA dynamics, one for each factor. We give theoretical results on the stable fixed points of this system and show experimental results on invariant object recognition.