Investigations of multi-robot systems often make implicit assumptions concerning the computational capabilities of the robots. Despite the lack of explicit attention to the computational capabilities of robots, two computational classes of robots emerge as the focal points of recent research: Robot Ants and robot Elephants. Ants have poor memory and communication capabilities, but are able to communicate using pheromones, in effect turning their work area into a shared memory. By comparison, Elephants are computationally stronger, have large memory, and are equipped with strong sensing and communication capabilities. Unfortunately, not much is known about the relation between the capabilities of these models in terms of the tasks they can address. In this paper, we present formal models of both Ants and Elephant, and investigate if one dominates the other. We present two algorithms: AntEater, which allows Elephant robots to execute ant algorithms; and ElephantGun, which converts elephant algorithms—specified as Turing machines—into ant algorithms. By exploring the computational capabilities of these algorithms, we reach interesting preliminary results regarding the computational power of both models.