Müllerian mimicry has traditionally been thought to benefit both unpalatable mimic and model species but recently its existence has been questioned. Even if both mimic and model species are unpalatable, they are unlikely to be equally unpalatable. It has been argued that the more unpalatable species will suffer a cost of increased predation because the presence of the more palatable mimic will increase its perceived palatability (by the predator), similar to that experienced by a model in Batesian mimicry. Yet, previous models of Müllerian mimicry have assumed that a predator can discriminate perfectly between available prey. We argue that this is not the case and that discrimination error is an important factor in determining the nature of mimetic relationships. Using computer simulations we show that the nature of a mimetic relationship will depend on the trade-off between the cost of an increase in perceived palatability and the benefits of a reduction in predator discrimination error. We show that mimicry can be unequivocally Müllerian, with both species benefiting, and propose that palatability should no longer be used as the sole defining characteristic of a mimetic relationship. Copyright 1998 The Association for the Study of Animal Behaviour. Copyright 1998 The Association for the Study of Animal Behaviour.