The Armed Forces do more and more complicated operations with ground forces supported by air forces in the mountainous terrain on missions around the world. In order to reach a decision in battle local superiority should be achieved. However, there is nothing that says how it is achieved, depending on the terrain. Therefore, this paper examines how local superiority were achieved during operation Anaconda, which was an operation in mountainous terrain of modern times. On this basis, this paper will examine how the US achieved local superiority during Operation Anaconda, by analyzing the operation with the principles of war, massing and surprise, which, according to Vego's theory, allow local superiority to be achieved. The aim is to examine how local superiority can be achieved in mountainous terrain. The overriding question is therefore; how was local superiority achieved during operation Anaconda? The results shows that the terrain mainly affects the land units, because their mobility is reduced on the steep and inaccessible terrain. To achieve local superiority with ground units thus becomes difficult. The results show that it is important to use the right means and method. During Operation Anaconda the air force could achieve both principles of war, mass and surprise. As a result local superiority was achieved and the operation was successful. Therefore Close Air Support is a vital part to achieve local superiority in mountainous terrain.