In this paper we present a simple evolutionary model of childrens’ language development, whose central nonlinearity is represented by noninvertible discrete dynamical systems. The underlying assumption of the model is that children learn from other children through their interactions. The concrete learning mechanism used is based on imitation, where childrens’ languages evolve through attempting to imitate other childrens' utterances. The use of imitation in evolutionary models has been used, for instance, in evolution of bird song by Kaneko and Suzuki. The model to be presented here is similar to Kaneko and Suzuki’s model, the primary difference being the continuous nature of bird song, in contrast to the discrete nature of childrens’ utterances.