We propose that replication (with mutation) of patterns of neuronal activity can occur within the brain using known neurophysiological processes. Thereby evolutionary algorithms implemented by neuro- nal circuits can play a role in cognition. Replication of structured neuronal representations is assumed in several cognitive architectures. Replicators overcome some limitations of selectionist models of neuronal search. Hebbian learning is combined with replication to structure exploration on the basis of associations learned in the past. Neuromodulatory gating of sets of bistable neurons allows patterns of activation to be copied with mutation. If the probability of copying a set is related to the utility of that set, then an evolutionary algorithm can be implemented at rapid timescales in the brain. Populations of neuronal replicators can undertake a more rapid and stable search than can be achieved by serial modification of a single solution. Hebbian learning added to neuronal replication allows a powerful structuring of variability capable of learning the location of a global optimum from multiple previously visited local optima. Replication of solutions can solve the problem of catastrophic forgetting in the stability-plasticity dilemma. In short, neuronal replication is essential to explain several features of flexible cognition. Predictions are made for the experimental validation of the neuronal replicator hypothesis.