A thorough analysis of the inter-hemispheric Rooth 3-box model is performed in order to study the stability of the present northen sinking regime of the Thermohaline Circulation (THC) against perturbations to the atmospheric freshwater and heat fluxes. The perturbations lead the system to a newly established equilibrium that is either qualitatively similar to the initial one, i.e. a northern sinking equilibrium, or radically different i.e. presenting a reversed THC.We first analyze the uncoupled version of the model. High rates of increase in the poleward moisture flux in the Northern Hemisphere lead to a THC breakdown at smaller moisture fluxes than low rates, while increases in the poleward moisture flux in the Southern Hemisphere strongly inhibit the breakdown Similarly, heat flux increases in the Northern Hemisphere destabilize the system more effectively than slow ones, and again the heat flux increases in the Southern Hemisphere tend to drive the system towards stability. Thus in the case of realistic perturbations, e.g., in global warming scenarios, it is necessary to perturb the system in both hemispheres at the same time. Although there is an overall similarity between the effects of atmospheric freshwater and heat fluxes perturbation, a detailed comparison where the intensity of the two perturbations are rescaled in density unity shows that the thermal and saline way of destabilizing the THC are not fully equivalent. In the coupled version of the model (the Scott et al. model) the atmospheric freshatwater and heat fluxes depend of the temperatures of the boxes and are parametrized in a physically based way. The preliminary results obtained for this version of the model present interesting features both resembling and not resembling the results obtained for the uncoupled model. Complete results will be presented at the conference.