Environmental impacts of agricultural production, such as greenhouse gas (GHG) and nitrogen emissions, are of major concern for scientists and policy makers throughout the world. Global agricultural activities account for about 60% of nitrous oxide and about 50% of methane emissions. From a global perspective, methane and nitrous oxide constitute crucial GHGs. They contribute substantially to climate change due to their high potential for effecting global warming compared to carbon dioxide. Emissions of these gases depend on the extent of agricultural production and applied technologies. Therefore, analysis of potential mitigation opportunities is challenging and requires an integrated approach in order to link agricultural economic perspectives to environmental aspects. In view of this, a mathematical programming model has been developed which enables assessment of cost-effective strategies for mitigating GHG and nitrogen emissions in the agricultural sector in Switzerland. This model is applied to improve understanding of the agricultural sector and its behavior with changing conditions in technology and policy. The presented recursive-dynamic model mimics the structure and interdependencies of Swiss agriculture and links that framework to core sources of GHG and nitrogen emissions. Calculated results for evaluation and application indicate that employed flexibility constraints provide a feasible approach to sufficiently validate the described model. Recursive-dynamic elements additionally enable adequate modeling of both an endogenous development of livestock dynamics and investments in buildings and machinery, also taking sunk costs into account. The presented findings reveal that the specified model approach is suitable to accurately estimate agricultural structure, GHG and nitrogen emissions within a tolerable range. The model performance can therefore be described as sufficiently robust and satisfactory. Thus, the model described here appropriately models strategies for GHG and nitrogen abatement in Swiss agriculture. The results indicate that there are limits to the ability of Swiss agriculture to contribute substantially to the mitigation of GHG and nitrogen emissions. There is only a limited level of mitigation available through technical approaches, and these approaches have high cost.