Aggregation of dry cohesive powders and dissipation of energy during loading of the aggregates are under consideration. Under the influence of interparticle adhesion, fine particles of the powders cluster together to form simple agglomerates. The simple agglomerates adhere together to form larger, complex agglomerates, which in turn, may adhere together and form a hierarchical structure. It is shown that contrary to diffusion-limited colloid aggregation, the simple agglomerates consisting of alumna or titanium dioxide particles are not mass fractals. The core structure of the simple agglomerates is described as a non-ordered homogeneous structure with a constant volume fraction, while the outer part (shell) can be considered as a rough surface that may have quite extended protuberances. It is shown that the total energy dissipated during relative motion between simple agglomerates depends on the amount of the primary cycles - "jump into contact - pull off" between cohesive particles. Finally, the specific properties of cohesive powder dampers are discussed.