In this paper, we generalize the notion of a communication equilibrium (Forges 1986, Myerson 1986) of a game with incomplete information by introducing two new types of correlation device, namely extended and Bayesian devices. These new devices explicitly model the ‘thinking process’ of the device, i.e. the manner in which it generates outputs conditional on inputs. We proceed to endow these devices with both information processing errors, in the form of non-partitional information, and multiple transition and prior distributions, and prove that these two properties are equivalent in this context, thereby generalizing the result of Brandenburger, Dekel and Geanakoplos (1988). We proceed to discuss the Revelation Principle for each device, and conclude by nesting a certain class of ‘cheap-talk’ equilibria of the underlying game within Bayesian communication equilibria. These so-called fallible talk equilibria cannot be generated by standard communication equilibria.