In today’s modern conflicts air power has proven to be a major contributing factor towards success.Whether the conflict is of regular or irregular nature, air power has many positive attributes that canplay a crucial role in the result of the battle. However there are cases where air superiority wasachieved but the outcome of the conflict didn’t result in success. Which indicates that air power isn’talways the key to success. To examine this further it is necessary to test an air theory on two separatecases that are similar but different in one aspect, the outcome. The theory that is used to examinethe two cases is Robert Pape´s theory “Coercive by denial”, because this theory has been criticizedthat it does not function on modern and irregular conflicts. The purpose of this thesis is to implement Pape´s air theory “Coercive by denial” to see if this theorycan explain the differences in the outcome between the two battles of Fallujah in Iraq 2004 by usinga comparative case study. Although air superiority was achieved in both battles the first is considereda failure, the second a success. The results of the research show that the theory cannot explain why the second battle was successfuland the first one was a failure. The result shows that Pape´s statement about what to target first inan irregular conflict to have the highest effect against insurgents isn’t always right. The result showsthat the second battle was more focused on attacking the enemy’s logistics then the first battle. Thatcould be a reason why the second battle was a success but it is against Pape´s own statement in histheory. The main conclusion of the thesis is that “Coercive by denial” cannot explain the variationin the outcome of the battles of Fallujah, and Pape´s theory can be questioned. This indicates thenecessity of further studies on Pape’s theory on irregular conflicts