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This article explores the different models of progress discussed by Leibniz in two Latin texts written between 1694 and 1969. It shows the different conceptions of perfection that are implied by these two models, namely the hypothesis of a continual evolution of creatures and of a world without progress, and that of a universal perfection. Although the thesis of the best possible world holds regardless of which hypothesis is maintained, the Principle of the Best seems to favor the idea of the perpetual progress of the world, and permits us, if not to determine the particular form that this progress must take, at least to rule out certain models of evolution.