Chapter Five was devoted to the metaphysics that underpins the Stoic theories of everlasting recurrence. The present chapter focusses on three of these theories in some detail. At least two of them, as I explain in section 6, are early Stoic. As we shall see, one is stronger than the other two, and the two weaker theories are revisions of it. A central component of this chapter is the thesis of Identity, according to which there must be a full type-identity between the events of any two cosmic cycles. Why should this thesis be true? Why could not the events be slightly, or even completely, different? Thus, sections 1 and 2 describe the three theories and how exactly they differ from one another. In sections 3 and 4 are devoted to the argument for Identity. The argument is based on the nature of the Stoic god. It is his full rationality that requires that the token-events of each new cosmos be fully type identical to those of the previous one. I close the chapter in Sections 5-6 with a discussion of the two weaker theories. What are their philosophical motivations? And in what order did they emerge in the history of Stoicism?