This article seeks to show how several rhetorical tools were used and, in fact, played a central role in the argumentation advanced by Niles Eldredge and Stephen Jay Gould in their 1972 seminal article on the theory of Punctuated Equilibria. It is analyzed how Eldredge and Gould proceeded through three steps that, sequentially integrated, made their argument compelling. It is shown how they made use of analogies, metaphors and other rhetorical tools. It is sustained that they began by priming the reader to distrust the current interpretation of the fossil record offered by most paleontologists and then, in a second step, they used specific visual representations in order to suggest that the competitor theory was committed to the idea of an even and slow evolution at a constant rate, an image utilized by them as straw man. Finally, it is analyzed how, in their third step, Eldredge and Gould made use of several rhetorical arguments to present their theory as new for paleontology while, at the same time, placing it well inside the frame of the modern synthesis, and how they also managed to present their theory as more promising and capable of making predictions for future researches than the competitor theory.