This paper shows how Peirce's semeiotics can be applied to explain the representation of non-existent or unreal objects, whether in misrepresentation or in thought and discourse about fictional objects. Such representation would seem to require a relation between a sign and an unreal object, and the puzzle is how a real object (the sign) can bear a relation to an unreal object. Peirce can solve this puzzle without denying that representation generally is relational. However, he can deny that the representation of an unreal object involves a real relation to that object. The key lies with his distinction between the immediate object and the dynamical object of a sign, as an unreal object is always only an immediate object. With a functional substitution model of signs (suggested by Peirce's writings, and defended here) we can understand an unreal immediate object in terms of an interpreter responding to a sign as if it were related to a real object. The remainder of this Peircean solution rests upon a realist interpretation of dynamical objects, as well as upon his abstract definition of truth as the correspondence of a sign to its object, which helps to explain how some propositions about unreal objects can be true.