Two of Plato’s dialogues, the Parmenides and the Timaeus, deal explicitly with the relationship between being and time. The former builds on the assumption that whatever is must be temporal, while the latter makes being and time mutually exclusive. This paper begins by examining how the argument develops in the Parmenides, specifically in the corresponding sections 140e1-142a1 and 151e3-155e3 of the first and the second deductions of the dialectical exercise, as well as in the corollary to the second deduction at 155e4-157b5. It then compares this argument with the account of time given in Timaeus 37e6-39e2, which alludes to the account given in the Parmenides. In stressing the incompatibility of these two accounts, it highlights a remarkable feature they both share. Parmenides’ argument starts from the assumption that whatever is in time must be present, past or future, whether a process or a state resulting from a process. As he advances further in the game of Zenonian antilogies, however, he reduces the dimension of the present to a mere ‘now’, conceived of as a ‘stop’ in the process of becoming. In the corollary, he eventually removes the present from time the ‘instant’ in which a change between two mutually exclusive processes or states occurs. Timaeus, for his part, immediately rules out that the present is a temporal dimension, by restricting temporality to the past and the future. Thus, in both accounts, the present vanishes from time and temporal processes are made dependent on extratemporal conditions. However, Parmenides’ argument points to an extratemporal principle of indeterminacy allowing for change, while, for Timaeus, there are two extratemporal conditions for temporal processes, namely the being of the intelligible Forms, on the one hand, and a pre-cosmic, disorderly becoming in space, on the other.