This work investigates the use of Co-evolutionary Genetic Algorithms in the automation of the development process of object-oriented software systems. The software final quality depends mainly on the design quality developed for the same. During the design phase, different models are developed anticipating various visions of the end product, thus making possible the software evaluation before it is implemented. The synthesis of a software model can, therefore, be seen as an optimization problem where it seeks a better configuration between the contemplated elements for the object-oriented paradigm, as classes, methods and attributes, which follows the quality design criteria. The work goal was to study a way to synthesize designs of better quality through its evolution by Coevolutionary Genetic Algorithms. In order to assess the software quality, it was also investigated software quality metrics, such as: Reusability, Flexibility, Understandability, Functionality, Extensibility and Effectiveness. These metrics were applied in an evaluation function that, in turn, was defined aiming at the object-oriented design synthesis with a better quality. In this problem, it is desired to contemplate more than one objective at a time. For this, the Pareto technique for multi-objective problems was used. The results were compared with designs produced by specialists and its characteristics analyzed. The GA performance in the optimization process was compared with the exhaustive search and, in all cases, the model results were superior.