This paper develops a NATREX (NATural Real EXchange rate) model for two large economies, the Eurozone and the United States, which are fully specified and allowed to interact. After description of the theoretical framework grounding on dynamic disequilibrium modelling approach in continuous time, we implement empirical analysis. First, we estimate the model in its structural form as a simultaneous nonlinear differential equation system for the 1975-2003 period. Second, we simulate the Euro/USD NATREX series in- and out-of-sample by using parameters estimates. The simulated equilibrium real exchange rate enables us to determine a benchmark against which the dynamics of the actual real exchange rate can be measured.