On at least three different occasions, Peirce insisted on the necessity to admit the cyclical, i.e. self-returning nature of time (1.274, 1.498 and 6.210). This view is altogether incompatible with one essential aspect of his philosophy, i.e. with his tychism which unambiguously rejected the rigorous determinism of classical science; but this, as we shall see, was one of the basic assumptions of the cyclical theory of time. The fact that Peirce did not mention it, shows that he failed to grasp the full meaning of the cyclical theory of time; and this undoubtedly explains why his own arguments in favor of this theory are so obscure and unconvincing. (I shall return to his arguments at the end of this paper.)