The concepts of 'rational conjectures' and 'reasonable conjectures' are critically reviewed. It is shown that their operation depends crucially on an invisible, non-optimizing 'deus ex machina'. Hence, these concepts are not really suitable for understanding competition among optimizing firms. In addition, the widely claimed "fact" that Bertrand conjectures are locally rational conjectural variations is shown to be erroneous. THE MESSAGE of this paper should be plain from the title. It reflects a disillusionment with the concepts of 'rational conjectures' and 'reasonable conjectures', for helping us understand economic interactions under imperfect competition. On the face of it, these concepts seem to offer the economic modeller some useful tools. Hence this paper is in some sense intended as a friendly warning to other economic modellers. There are inherent conceptual weaknesses in these concepts, that do not become apparent until one begins to penetrate their inner logic. To make plain the weaknesses of 'rational conjectures' and 'reasonable conjectures', we shall concentrate on the simplest application of the ideas-to duopoly. And, we shall illustrate our points using the classical Cournot example of duopolists facing a common linear demand curve and having the same, constant marginal cost. The reader may know that this example figures prominently in the rational conjectures literature, it being "shown" that Bertrand conjectures are locally rational conjectural variations. We shall see in section VI that this claim is not really valid, although widely asserted. But our real message is on a different plane, and pertains to the usefulness of the concepts in general.