As urban systems are complex systems, their further evolution cannot be merely a linear projection of the most recent trends, nor can it be taken for granted that the future will replicate what happened in the past. Nor can we reliably predict the evolution of European cities by looking at those in North America. We have developed a new theory, at a conceptual level, which can not yet be entirely formalised in a mathematical way but which can be experimented with agent based simulation models. We present here the main principles of the conception of the model and the first results of its experimentation. Our ambition is first to reproduce the evolution of urban systems in different parts of the world, second to use this validated tool for exploring the future evolution of cities under a variety of hypothesis about changes in the local or global context.