In general, Evoluationary Algorithm(EAs) are refered to as methods of population-based optimization. And EAs are considered as very efficient methods of optimal sytem design because they can provice much opportunity for obtaining the global optimal solution. This paper presents a co-evolution scheme of artifical neural networks, which has two different, still cooperatively working, populations, called as a host popuation and a parasite population, respectively. Using the conventional generatic algorithm the host population is evolved in the given environment, and the parastie population composed of schemata is evolved to find useful schema for the host population. the structure of artificial neural network is a diagonal recurrent neural netork which has self-feedback loops only in its hidden nodes. To find optimal neural networks we should take into account the structure of the neural network as well as the adaptive parameters, weight of neurons. So we use the genetic algorithm that searches the structure of the neural network by the co-evolution mechanism, and for the weights learning we adopted the evolutionary stategies. As a results of co-evolution we will find the optimal structure of the neural network in a short time with a small population. The validity and effectiveness of the proposed method are inspected by applying it to the stabilization and position control of the invered-pendulum system. And we will show that the result of co-evolution is better than that of the conventioal genetic algorithm.