This paper presents a computational investigation of the short-term and long-term behaviour of the Oklo natural nuclear reactors, instances in the distant past in which natural uranium deposits developed self-sustaining nuclear chain reactions. For the first time, processes occurring on timescales of seconds (such as changing temperature, moderator availability and power) are coupled in a single simulation with processes occurring over timescales of thousands of years (such as changing enrichment, reactor geometry and isotopic composition). This simulation reproduces key features of the Oklo reactors found in the literature (the cyclic boiling and flow of water in and out of the reactor; the characteristic three-hour cycle time; the total energy released by the reaction), gives greater insight into their development and evolution, and demonstrates a non-cyclic, non-boiling regime of behaviour in the later stages of reactor operation that has not previously been described.