This article develops a dynamic optimising macro model of a open economy specialised in tourism based on natural resources. Environmental externalities are explicitly introduced in the production function. Global dynamic analysis shows that, under some conditions on the parameters, if the initial values of the state variables are close enough to the coordinates of Pa, then there exists a continuum of equilibrium trajectories approaching Pa and one trajectory approaching Pb. Therefore, the model exhibits global indeterminacy, since either Pa or Pb can be selected according to agent expectations.