The use of adhesively bonded structures has increased over the years, together with the development of composite materials. This work investigates a procedure for fatigue life prediction of an aeronautical bonded joint under random loads, in particular, the cohesive failure of the adhesive layer in a skin-to-stiffener bonded joint. The use of two different adhesives is investigated, and Dirlik’s method is employed to predict the stress response in the adhesive layer, from which the fatigue life is obtained. The effect of damping is also investigated, and it is shown that increases in damping result in higher fatigue life estimations.