This paper deals with the modeling of economy-environment interactions for several countries which are assumed to behave competitively for the control of their own economic processes but have to achieve jointly a common environmental management goal. The paper is organized in two parts treating of modeling issues related to process dynamics and players interactions respectively. In the first part we discuss the control theoretic approach for representing the economic and pollution processes in a model of environmental management. We also give a short discussion of a possible representation of uncertainty and risk in these models. In part two we propose a dynamic game modeling approach which combines two classic models, the N-person equilibrium model with coupled constraints proposed by Rosen and the differential game model with active and passive variables proposed by Brock. These models permit the definition of a tax scheme which induces a set of equilibrium seeking players to achieve, in the long run, a global environmental goal.